Born in Glasgow in 1907, Graham Murray began his artistic education at the Glasgow School of Art. On completion of his studies, Murray spent several years exploring the European Continent, living and working in Turkey, Switzerland, Germany and France before returning to his native Glasgow in 1938. Murray taught for some time at the Port Glasgow High School in the industrial Scottish city of Clydebank during the Second World War, an experience which may have influenced his futurist approach to painting. During this time his close friendship with the artist Stanley Spencer, who himself was on commission painting the shipyards of Clydebank, also provided a great source of inspiration. Murray participated in several exhibitions at the Leicester and Lefevre Galleries in London.

In his native Scotland Murray received great acclaim as an artist, and he exhibited throughout his career with both the Royal Scottish Academy and the Royal Glasgow Institute of Fine Arts throughout his career. In 1985 Murray moved to Berkshire, England where he lived and worked for the rest of his life. His work is represented in numerous collections throughout Britain.