Trans-1,4-polybutadiene is normally synthesized utilizing transition metal or rare earth catalysts. However, molecular weight control is difficult to achieve with such catalysts and the molecular weight of the polymer produced is frequently much higher than desired. By utilizing the catalyst system and techniques of this invention, trans-1,4-polybutadiene can be synthesized continuously to a high level of conversion with molecular weight control being possible. This invention specifically relates to a process for synthesizing trans-1,4-polybutadiene by polymerizing 1,3-butadiene monomer in the presence of a catalyst system which is comprised of an organocobalt compound, an organoaluminum compound and a para-substituted phenol with molecular weight being controlled by conducting the polymerization in the presence of at least one dialkyl sulfoxide, diaryl sulfoxide or dialkaryl sulfoxide. Such polymerizations can be conducted on a batch or a continuous basis. In the case of continuous processes, it is normally desirable to conduct the polymerization in the presence of carbon disulfide as a gel inhibitor.