Born in Edinburgh, Crozier studied at Edinburgh College of Art, a friend and fellow student of Anne Redpath, William Gillies and William MacTaggart. Crozier lived in Paris in 1923, while on a Carnegie Travelling Scholarship, and studied with the cubist painter André Lhote. He also travelled to Italy, where he was captivated by the bright sunlight which cast deep shadows. Crozier later attempted to capture this intense light, as he was to adopt the lessons of Cubism, in his own work. After suffering ill health all his life due to haemophilia, Crozier died, aged just thirty-seven, following a fall in his studio.