The present invention relates to the preparation of syndiotactic 1,2-polybutadiene polymer using a catalyst containing a carbon disulfide in which the polymerizate thereof is treated with hydrogen peroxide, to preparation of a composite of conjugated diene-based elastomer and syndiotactic 1,2-polybutadiene polymer using a catalyst containing a carbon disulfide which the polymerizate thereof is treated with hydrogen peroxide, a rubber composition containing said syndiotactic 1,2-polybutadiene polymer and/or said composite and a tire having at least one rubber component thereof.