James Robert Madison Mullany (26 October 1818 – 17 September 1887) was a rear admiral of the United States Navy, who served during the American Civil War.

Mullany was promoted to commander on 18 October 1861, and assigned to the side-wheel steamer Bienville in the North Atlantic and West Gulf Blockading Squadrons in April 1862.

From April till September 1863, he commanded a division of the West Gulf Squadron, and during the war captured eleven blockade-runners, and cut out two schooners laden with cotton in the harbor of Galveston, Texas.

In August 1864 Mullany commanded the screw sloop Oneida during the Battle of Mobile Bay, the Bienville being considered unfit to engage the forts by Admiral David Farragut.

After receiving his rear admiral's commission on 5 June 1874, he commanded the North Atlantic Squadron until February 1876, protecting American interests on the Isthmus of Panama.