A catalyst for polymerization of olefin, which is capable of producing an olefin polymer with high stereoregularity and narrow molecular weight distribution, and which comprises (1) a solid catalyst component essentially containing titanium, magnesium and halogen, 2) an organoaluminum compound, and (3) a contact product of (A) an organometallic compound and (B) an organosilicon compound; and a process for producing a polymer using the above catalyst.