To provide a production process, whereby a 1,2-polybutadiene polymer having a controlled m.p. is produced at a high activity even in a hydrocarbon solvent by using a specific catalyst system of which the cocatalyst can easily be produced.

1,3-Butadiene is polymerized in a hydrocarbon solvent in the presence of a catalyst system which comprises a cobalt salt-triarylphosphine complex catalyst component and an organoaluminum cocatalyst component obtd. by bringing trimethylaluminum into direct contact with water at -80 to 50°C in a hydrocarbon solvent and heating the resultant product at 60-200°C.