Disclosed is a process for the preparation of a high stereospecific (isotactic) polybutylene polymer comprising the step of polymerizing a reactive monomer, 1-butene, which is used or is not used as a solvent, in the presence of catalyst and inert gas. According to the present invention, it is possible to prepare a high stereospecific polybutylene polymer in much higher activity than that of any other known processes for the preparation of a high stereospecific polybutylene polymer. The high stereospecific polybutylene polymer according to the present invention is a homopolymer of 1-butene, or a copolymer containing a-olefin and up to 40% by weight of a comonomer, wherein titanium in the catalyst residues is not detected in the ppm level, stereospecificity (Isotactic Index, mmmm %) determined by .sup.13C-NMR is 96 or more, molecular weight distribution (Mw/Mn) is 3-6, and molecular weight distribution (Mw/Mn) can be controlled to 8 or more.