There are provided (1) a process for producing a solid product, which comprises the step of reducing a titanium compound represented by the following formula [I] with an organomagnesium compound in the presence of an organosilicon compound having an Si--O bond, an inorganic fine particle and optionally an ester compound, ##STR1## (2) a process for producing a solid catalyst component, which comprises the step of contacting the solid product obtained by the above process, a halogenation ability-carrying halogeno compound, and an inner electron donor compound, (3) a process for producing a catalyst, which comprises the step of contacting the solid catalyst component obtained by the above process, an organoaluminum compound, and an outer electron donor compound, and (4) a process for producing an olefin polymer, which comprises the step of polymerizing an olefin in the presence of the catalyst obtained by the above process.