Sir Henry appears to have been the younger son of a London wealthy baker, John Marten, and his wife, Rose. The suggestion that he was the  son of Anthony Martin (sic), Citizen of London, by Anne, the daughter of John Jacob of Bishop's Stortford in Hertfordshire, is now considered unlikely. This despite James Yate of Buckland being recorded as a 'cousin' and Anthony's parents being William Martin Esq. of Wokingham and Margaret, the daughter of John Yate of Charney Manor and Lyford Grange. He was born in the parish of St. Michael Bassishaw, London, probably in 1562, was educated at Winchester School and New College, Oxford, where he matriculated on 24th November 1581, aged 19, and was elected to a fellowship in 1582. He had also a little property in London, left him by his father, worth £40 a year. By the advice of Lancelot Andrewes, he applied himself to the study of the civil and canon law, and adopted the practice of holding weekly disputations on moot points raised by cases pending in the high commission court. He graduated BCL in 1587 and DCL in 1592, and was admitted a member of the College of Advocates on 16th October 1596. In August 1605, he took part in the disputations held before the king at Oxford. Marten early acquired an extensive practice in the admiralty, prerogative, and high commission courts, and was appointed official of the archdeaconry of Berkshire. On 3rd March 1609, he was made King's advocate, and, in March 1613, he was employed on a mission to the Palatinate in connection with the marriage settlement of the Lady Elizabeth. He was appointed chancellor of the diocese of London in 1616, was knighted at Hampton Court on 16th January 1617, and in the following October was made judge of the admiralty court. He was one of the commissioners appointed in January 1619 to negotiate a treaty of peace between the English and Dutch East India Companies, and in common with his colleagues was thought to have sold the interests of the English company for money.

In the devious ways of a Stuart judge, Henry amassed a fortune which he invested wisely in land in north-west Berkshire where his grandmother's family came from. His first purchase was in the Vale of the White Horse, at West Challow. His second was the manor of Longworth which he bought for £9,500 in 1618. His third was Hinton Waldrist Manor, a Crown lease of which he obtained for £37-16s-8d. He built  Longworth House which became his principal residence.

On 29 April 1620 Marten was placed on the high commission. He also sat on the special commission which in October 1621 tried and determined in the negative the curious question whether Archbishop Abbot was incapacitated for his functions by his involuntary homicide. As judge of the admiralty court the case of Sir John Eliot and the pirate Nutt came before him in July 1623, but only on a special reference to take the necessary evidence and report to the privy council. His conduct in keeping strictly within the terms of the reference, and expressing no opinion on the merits of the case, has, on insufficient grounds, been censured as subservient. On 4th August he wrote to Secretary Conway, urging Eliot's release on bail, and as he had not to try the case it is not clear that he could have done more. His subsequent relations with Eliot were those of close friendship. In September 1624 he was one of the commissioners for the settlement of the Amboyna affair. The same month Archbishop Abbot conferred upon him the places of dean of the arches and judge of the prerogative court of Canterbury, vacant by the death of Sir William Bird (5th September), both of which he retained on the deprivation of the archbishop 9 Oct. 1627. He stood well with King James, who complimented him ' as a mighty monarch in his jurisdiction over land and sea, the living and the dead.'

Marten entered parliament as member for St. Germans, Cornwall, on 22 April 1625, and made his maiden speech at the opening of the Oxford session on 1 Aug., when he supported Eliot in the attack upon the Duke of Buckingham. His tone, however, in this and succeeding debates was studiously moderate. Nevertheless, in the next parliament, to which he was again returned for St. Germans (16th January 1626), an attempt was made to exclude him on the ground of his complicity in the committal of Sir Robert Howard by the high commission during the prorogation of parliament in March 1625. He was, however, allowed to take his seat on pleading ignorance of the distinction - in regard to matters of privilege - between prorogation and dissolution. He sat for the university of Oxford in the parliament of 1628, and took an important part in the debates on the Petition of Right. His speech against the lords' addition at the conference of both houses on 23rd May - a masterpiece of tact, firmness, and moderation - is printed in Rushworth's 'Historical Collections,' and the 'Parliamentary History'. Though he had come into sharp collision with the Duke of Buckingham in the matter of a French ship, the St. Peter of Newhaven, seized on suspicion of carrying Spanish goods, and illegally detained by the duke's orders. Marten, nevertheless, opposed (13th June 1623) the insertion in the Remonstrance of a clause expressly censuring the duke. In January 1629 he was placed on the committee of inquiry as to the affair of the Clerkenwell Jesuits.

Though reputed the first civilian of his time, Marten was much hampered in the administration of the admiralty court by writs of prohibition issuing from the king's bench, against which he unsuccessfully appealed to the king in Easter term 1630. He was one of the commissioners for the repair of St. Paul's appointed 10th April 1631, and sat in the Painted Chamber as judicial assessor to the court of chivalry on the trial of Lord Reay's appeal of battle against David Ramsay on 28th November following. He had a hand in the revision of the statutes of the university of Oxford, the title, 'De Judiciis,' being referred to him by the revisers in 1633, and was one of the commissioners through whom the completed work was transmitted by the king to the university in June 1636. He argued before the privy council for several days 'with his utmost skill,' says Clarendon, against the validity of the 'new canons' framed by convocation after the dissolution of the Short parliament of 1610. In that parliament he sat for St. Ives, Cornwall, but was not returned to the Long parliament, by which he was fined £250 for his part in the imprisonment of Sir Robert Howard.

Marten was superseded by Sir John Lambe as dean of the arches in the autumn of 1633, but retained his place in the high commission court until its abolition by the Long parliament, and the judgeship of the admiralty and prerogative courts until his death on 26th September 1641. He was buried in the parish church of Longworth, Berkshire, where was his principal seat. He had several other estates in the same county. His town house was in Aldersgate Street. Gayton termed him ambiguously 'the blue-nosed Romanist.' At his death several petitions charging him with misfeasance in his various judicial capacities were pending in the House of Lords. By his wife, Elizabeth Weld, who died on 19th June 1618, Marten had issue, two sons, Henry and George, and three daughters, Elizabeth, Jane, and Mary. Some of Sir Henry's decisions have been printed for the Camden Society in ' Cases in the Courts of Star Chamber and High Commission,' and ' Documents illustrating the Impeachment of the Duke of Buckingham.' Marten's name is frequently spelt Martin.