A process for producing .alpha.-olefin polymers with a controlled stereoregularity and with a higher yield is provided, which process comprises: combining a TiCl.sub.3 -containing composition obtained by reducing TiCl.sub.4, with an organoaluminum compound; thereafter subjecting the composition to a polymerization treatment with an .alpha.-olefin; before, during or after the polymerization treatment, adding an electron donor or/and an electron acceptor or a reaction product of these two; as well as adding a reaction product of a trialkylaluminum with an electron donor having a specified molar ratio of the electron donor to the trialkylaluminum selected in the range of 0.01 to 5; and polymerizing an .alpha.-olefin in the presence of the resulting preactivated catalyst.