PURPOSE: To prepare olefin polymer without requiring a catalyst-removing process and an extracting process of amorphous polymer by polymerizing olefin in the presence of a catalyst comprising a specific solid halogen-containing product and an organometallic compound.

CONSTITUTION: Magnesium halide such as MgCl, MgBr or the like, an electron- donor compound such as carboxylic acid ester, sulfonic acid chloride or the like and a boron compound represented by a formula (wherein R is 1W14C hydrocarbon residue; X is hologen; n is 1W3) are ground together at 0W100°C for 2W100hrs. and thereafter a Ti compound such as TiCl4, Ti(O-CH3)Cl3 or the like is added and ground at room temperature to 100°C for 1W100hrs. to obtain a halogen-containing solid product (A). Subsequently, in the presence of a catalyst comprising a halogen-containing solid product (A) and an organometallic compound (B) of metal belonging to IWIII group of periodic toble, olefine is polymerized at 30W200°C under atmospheric pressure to 100atm.