Polymerization of olefins and catalyst therefor, said catalyst comprising polymerizing at least one member selected from the group consisting of ethylene, propylene, butene-1 and styrene in the presence of a catalyst composition comprising (1) an organoaluminum compound having the formula, AIR2X wherein R represents a hydrocarbon residue selected from the group consisting of alkyl, aryl, aralkyl, alkaryl and cycloalkyl groups and X represents a halogen atoms selected from the group consisting of chlorine, bromine and iodine, (2) a halide of a transition metal of Groups IV, V and VI of the Periodic Table of the Elements, and (3) an aliphatic carboxylic ester having a side chain on a carbon atom in a Alpha -position to the ester carbon atom, the molar proportion of said organoaluminum compound, said halide of transition metal and said aliphatic carboxylic ester being 10-0.5 : 1 : 0.01-1.