An α-olefin polymer having extremely high stereoregularity, exhibiting excellent fluidity and containing a decreased amount of catalyst residues in the polymer can be obtained industrially advantageously in accordance with a process for producing an α-olefin polymer which comprises homopolymerizing an α-olefin or copolymerizing two or more α-olefins in the presence of (A) a solid catalyst component comprising magnesium, titanium and a halogen, (B) an organoaluminum compound having a content of hydroaluminum compounds of 0.1% by weight or smaller and (C) an organozinc compound.A block copolymer of propylene comprising a homopolymer portion exhibiting high fluidity and a copolymer portion having a high molecular weight can be obtained in accordance with a process for producing a block copolymer of propylene which comprises polymerizing propylene in the presence of (A) a solid catalyst component comprising a titanium compound and an electron-donating agent, (B) an organoaluminum compound and (C) an organozinc compound to produce crystalline polypropylene and copolymerizing propylene and at least one of ethylene and α-olefins having 4 or more carbon atoms in the presence of the produced crystalline polypropylene.