James A. Greer (28 February 1833 - 17 January 1904) was an admiral in the United States Navy who served during the Civil War.

Born in Cincinnati, Ohio, Greer enlisted in the Navy in 1848. He entered the Naval Academy in 1853 and graduated as a Passed Midshipman the following year. After participating in the Paraguay Expedition , he cruised the west African coast until the outbreak of the Civil War.

Greer was serving on board San Jacinto 7 November 1861 when she stopped the British steamer Trent and removed the Confederate commissioners on their way to England, thereby nearly drawing Great Britain into the war on the Confederate side. Greer served in St. Louis from 1862 to 1863 and was then attached to Rear Admiral David Porter's Mississippi Squadron . While in command of the ironclads Carondelet and Benton , he participated in the Vicksburg campaign and the shelling of Grand Gulf as well as the abortive Red River expedition . After commanding the Naval Station at Mound City, he assumed command of the flagship Blackhawk and then was in charge of conveying Army transports up the Tennessee River.

A tour of duty as Assistant to the Commandant at Annapolis after the war was followed by command of Mohongo on the Pacific Station, where Greer was commended for "defending American interests" in Mexico. After duty at the Naval Academy between 1869 and 1873, Greer returned to the Pacific Station. In 1873 he commanded Tigress when that ship was sent to find and aid Polaris. Polaris was wrecked on an Arctic expedition which had been led by Charles Francis Hall. After special service in Constitution during the Paris Exposition , Greer held a variety of shore posts and then served as commander of the European Squadron from 1887 to 1889.

Promoted to Rear Admiral in 1892, he retired 28 February 1895. Admiral Greer died in Washington 17 January 1904.

USS Greer (DD-145) was named for him.