Since Cp*TiMe2(O-2,6-(Pr2C6H3)-Pr-i) (2) exhibited higher initial catalytic activity than Cp*TiCl2(O-2,6-(Pr2C6H3)-Pr-i) (1) for l-hexene polymerization in the presence of MAO, the effect of cocatalyst for the polymerization was investigated at low temperature (0 to -30 degreesC). The use of (AlBu3)-Bu-i/Ph3CB(C6F5)(4) was found to be effective to improve the activity and a notable increase in the activity was obtained if 2 was pre-treated with 2 equivalent of (AlBu3)-Bu-i in advance. TON (Turnover number) of is 100 (activity: 5710 kg-polymer/mol-Ti h) could be attained after 16 min under the optimized conditions and the M-n value for the resultant poly(1-hexene) increased upon the consumption of 1-hexene suggesting the possibility of living polymerization,