A process is described for obtaining a 1,3-butadiene homopolymer by the reaction of a catalytic system in the presence of 1,3-butadiene and one or more monoolefin(s) with 4 carbon atoms. This catalytic system is based on at least: a conjugated diene monomer, an organic phosphoric acid salt of one or more rare earth metals, said salt being in suspension in at least one inert, saturated and aliphatic or alicyclic hydrocarbon solvent, an alkylating agent of the formula AlR.sub.3 or HAlR.sub.2, where R is an alkyl group, and an alkylaluminum halide halogen donor.