Abstract: A process for producing an ethylene polymer comprising bringing ethylene or ethylene and an .alpha.-olefin having 3 to 10 carbon atoms into contact with a catalyst comprising the following components (A) and (B):component (A): a solid component for a Ziegler type catalyst obtained by bringing a solid product obtained by sequentially contacting the following components (A-1), (A-2) and (A-3) and then washing the contact product formed into contact with the component (A-4):component (A-1): a solid catalyst component comprising the following components (i), (ii) and (iii) wherein component (i) is a magnesium dihalide; component (ii) is a titanium tetraalkoxide and/or a polytitanic acid ester;and component (iii) is a polymeric Si compound represented by the formula: ##STR1## (R.sup.1 : a hydrocarbyl group) component (A-2) which is an organoaluminum compound; component (A-3) which is a silicon halide; and component (A-4) which is an organoaluminum halide; and component (B) which is an organoaluminum compound.