A process for preparing an ethylene polymer which comprises polymerization of ethylene or ethylene and an .alpha.-olefin having 3 to 10 carbon atoms over a catalyst comprising the following components (A) and (B): (A) which is a solid component for a Ziegler catalyst obtained by bringing (2) into contact with (1) and bringing the contact product into contact with (3) and (4) wherein (1) is a solid catalyst component comprising (i)-(iii) where (i): MgX.sub.2, (ii): titanium tetraalkoxide and/or a polytitanate ester, (iii): a polymeric silicon compound, having a formula of ##STR1## R.sup.1 being a hydrocarbyl group, (2) is a halogenated Si compound; (3) is a halohydrocarbon; (4) is an organo-Al compound; and (B) is an organo-Al compound.An ethylene polymer having a moderately broad molecular weight distribution can be prepared in a high activity by use of the catalyst. The ethylene polymer is suited for the production of fibers or tapes.