To obtain a catalyst for α-olefin polymerization capable of providing an α-olefin polymer having an extremely high stereoregularity in high yield and provide a method for polymerizing the α-olefin by using the catalyst.

This catalyst for an α-olefin polymerization is obtained by combining (A) a solid catalyst component obtained by bringing a component (A1) which is a solid component for α-olefin polymerization consisting essentially of titanium, magnesium, a halogen and an electron donor into contact with (A2) a silicon compound represented by the formula R1R23-mSi(OR3)m [R1 is an aliphatic hydrocarbon group adjacent to silicon atom; R2 is same or different hydrocarbon group or heteroatom-containing hydrocarbon group as R1; R3 is a hydrocarbon group; 1≤(m)≤3 with (B) an organoaluminum component and (C) a silicon compound component represented by the formula R42Si(OR5)2 (R4 is an aliphatic hydrocarbon group; R5 is a hydrocarbon group).