Abstract: In this article,based on the Taylor expansions of generating functions and stepwise refinement procedure,authors suggest a algorithm for finding the Lie and high (generalzed symmetries of partial differential equations (PDEs).This algorithmtransforms the problem having to solve over-determining PDEs,This algorithmand difficulty part in standard methods into one solving to algebaic equations towhich one easy obtain solution,So,it reduces significantly the difficulties of the problem and raise computing efficiency.The whole procedure of the akgorithm is carried out automatically by using any computer algebra system.In geeneral,this algorithm can yields many more important symmetries for PDEs.

Key words: Lie groups, high symmetries, Taylor polynomial, computer algebra, determining equations, stepwise rdfinement.