He was born in Glasgow and attended Westminster School and Glasgow University and entered the Army Medical Service. He served in India, where he studied enteric fever and kala azar. He returned to England and was stationed at the Victoria Hospital in Netley in 1897. In 1900 he was made Assistant Professor of Pathology in the Army Medical School, and described a method of staining blood for malaria and other parasites -- a modification and simplification of the existing Romanowsky method using a compound of Methylene Blue and eosin, which became known as Leishman's stain.
In 1901, while examining pathologic specimens of a spleen from a patient who had died of kala azar he observed oval bodies and published his account of them in 1903. Charles Donovan of the Indian Medical Serrvice independently found such bodies in other kala azar patients, and they are now known as Leishman-Donovan bodies, and recognized as the protozoan which causes kala azar, Leishmania donovani. Synonyms for kala azar now include leishmaniasis.
Leishman also helped elucidate the life cycle of Spirochaeta duttoni, which causes African tick fever, and, with Almoth Wright, helped develop an effective anti-typhoid innoculation.
Leishman is buried in Highgate Cemetery in London.