In accordance with the present invention, there are provided carrier-supported titanium catalyst components containing magnesium, aluminum, halogen and titanium as essential ingredients, which are obtained by a reaction of[I] a magnesium containing support obtained by previously bringing a support into contact with an organometallic compound of a metal of the Group II to IIIA of the periodic table having at least one hydrocarbon group attached directly to the metal atom or with a halogen containing compound, followed by contact with a magnesium compound in the liquid state having no reducing ability,[II] a reducing organometallic compound, and[III] a titanium compound in the liquid state, and processes for preparing the same and, at the same time, catalysts containing the above-mentioned catalyst components for use in preparing ethylene polymer and processes for preparing ethylene polymer using the catalyst for use in preparing ethylene polymer.