A novel olefin polymerization catalyst is provided which comprises (A) a transition
metal compound or lanthanoid compound containing two or more atoms selected from
the group consisting of boron, nitrogen, oxygen, phosphorus, sulfur, and selenium;
and (B) a Lewis acid. A process for producing an olefin polymer is also provided.
The catalyst has a high olefin polymerization activity without a combined use of
an expensive organoaluminum oxy-compound or organoboron compound, and can maintain
the high activity for a long polymerization time.