He was born at Goudhurst in Kent on 7 January 1755. He succeeded when about 21 to the business in West Smithfield of a linendraper named Greenland, to whom he had been apprenticed. Later, and until 1816, he was a successful West India merchant. He lived mainly at Goudhurst, where he built a small observatory; but moved to Blackheath in 1802.
Groombridge died in Blackheath. His Catalogue of Circumpolar Stars was published posthumously in 1838 with the help of fellow astronomer George Biddell Airy (1801–1892) and others. An earlier edition had been published in 1833 but was found to contain errors and was withdrawn. In 1842, one of the stars in his catalogue, Groombridge 1830, was discovered by Friedrich Wilhelm Argelander to have a very high proper motion. For many decades its proper motion was the highest known; today it still occupies third place.