This invention relates to a method for the selective hydrogenation of the unsaturated double bonds in the conjugated diene units of a homopolymer or copolymer in the presence of a novel homogeneous organotitanium-based catalyst. Also, the process of this invention can demonstrate a high yield of hydrogenation and hydrogenation reproducibility using a novel catalyst, so prepared from a mixture consisting of a substituted or unsubstituted monocyclopentadienyl titanium compound expressed by the following formula 1 and lithium hydride derived from a reaction of both alkyl lithium and hydrogen in solution. In particular, this invention also relates to a novel method for the selective hydrogenation of unsaturated double bonds in the conjugated diene units of a conjugated diene polymer or copolymer, so prepared via the reaction between a conjugated diene monomer and vinyl-substituted aromatic monomerwherein, R1, R2, R3, R4 and R5, which may be same or different, are selected from hydrogen atoms and alkyl groups of 1~5 carbon atoms; X1, X2 and X3, which may be same or different, are selected from halogen atoms.