PURPOSE: To provide a high purity α-olefin polymer by polymerizing gaseous α-olefin with in the presence of a specific catalyst system.

CONSTITUTION: A catalyst series in provided by combining (a) a solid catalyst precursor containing polycarboxylic acid ester which contains Mg, Ti, a halogen, and two ester groups coupled to neighboring C on the same plane, (b) hydrocarbylaluminum compound, and (c) Si-containing compound containing at least one C combined with Si through O, are combined so as to be in atomic ratio of Al:Si=0.5:(1-100), Al:Ti=(5:1)-(300:1). Next, one or more gaseous α-olefins are polymerized such under a condition that α-olefin partial pressure of below 70kg/cm2, at 30-120°C, the retention time of 1-20 hours, flow gas velocity of 0.03-1.5m/s.