PURPOSE: To produce polyolefins having a broad or multiple molecular weight distributions efficiently under a simpler condition such as a single reactor.

CONSTITUTION: The solid catalyst component active in combination with a suitable cocatalyst and an optional modifier in polymerizing 1-olefins is obtained by catalyzing a particulate comprising a solid support material with a quardrivalent zirconium compound of complex and, then, treating the resulting reaction product with a titanium or vanadium compound. The solid catalyst component does not having a precipitated magnesium value, constitutes a dual site catalyst component and constructs a catalyst system by using it, whereby a variety of 1-olefins are polymerized by using the catalyst system and the object polyolefins can be obtained.