A three-quarter-length portrait to left in a brown silk coat fastened with gold clips and with a gold-tasselled red sash round his waist. He is leaning forward onto a stone plinth, his right hand fingering his neck cloth. His telescope rests on the plinth in front of him, and there is a ship beyond. In the right background is a globe and brown draperies.

Smith fought as a captain against the Dutch in the First Dutch War and in the Second he commanded the 'Mary', 62 guns, at the Battle of Lowestoft in 1665. He was Admiral of the Blue squadron in the Four Days Fight and the St James's Day Fight in 1666. Smith quarrelled bitterly with Sir Robert Holmes who accused him of cowardice. The portrait is inscribed 'Sir Jeremiah Smith', and it is one of the 'flagmen' portraits commissioned by Charles II's brother James, Duke of York, after the Battle of Lowestoft.

This was the first major action of the Second Dutch War, in which James commanded the fleet. When Pepys visited Lely's studio on 18 April 1666 it was referred to in his diary, with those of Sandwich and Penn, as the three 'flagmen' portraits not yet begun.

Lely, a Dutchman who arrived in England in 1641 after the death of Van Dyck, soon became his successor as leading portraitist of the day. He worked for Charles I, continued to flourish under the Commonwealth and Protectorate, and after the Restoration of 1660 was appointed Principal Painter to Charles II. The full 'flagmen' set consists of thirteen individual portraits, of which George IV presented eleven plus a copy of that of Admiral Sir John Lawson (BHC2833) to Greenwich Hospital in 1824. The originals of Lawson and of Prince Rupert were retained in the Royal Collection, although William IV presented an extended full-length copy of the latter (BHC2990) to the Hospital in 1835.