The present invention provides a polymer in which coumarin, a photo-reactive molecule, is grafted onto a polyimide for preparing liquid crystal alignment layer which has a superior alignment property and an excellent thermal stability in photo-alignment, a process for preparing the said grafted polymer, a process for preparing liquid crystal alignment layer by employing the said grafted polymer, and a liquid crystal alignment layer prepared by the process. The polymer of the invention is prepared by mixing a coumarin compound with a polyimide, dissolving the mixture in an organic solvent, adding a catalyst, and stirring under an environment of N.sub.2 gas. The polymer of the invention is superior in terms of the thermal stability, which makes possible its universal application for the development of a novel liquid crystal display(LCD).