An optically active polymer is obtained by polymerizing a vinyl monomer in the presence of a catalyst which comprises an asymmetric ligand compound of the formula (I) or (II): ##STR1## in which R1 and R4 each are ##STR2## R2, R3, R5, R6, R7 and R8 each are an alkyl group having 1 to 10 carbon atoms; X is hydrogen, an alkyl group having 1 to 10 carbon atoms or a halogen; and n is a number of 1 to 4