To obtain a mixture of a high-molecular weight polybutadiene component and a low-molecular weight polybutadiene component in a high polymerization activity, useful as a rubber component for an impact-resistant polystyrene- based resin, by polymerizing butadiene by using a polymerization catalyst comprising a specific component.

Butadiene is polymerized in the presence of a catalyst comprising (A) a metallocene type complex of a transition metal compound and (B) an ionic compound of a non-coordinating anion and a cation and/or an aluminoxane to give a mixture which has 4-30% of 1,2-structure content, 65-95% cis-1,4-structure content and ≤5% trans-1,4-structure content and is composed of (C) a polybutadiene having 500,000-5,000,000 weight-average molecular weight (Mw) measured by gel permeation chromatography and (D) a polybutadiene having 2,000-300,000 Mw measured by GPC.