A solid catalyst component for olefin polymerization in which the molar ratio of residual alkoxy groups to supported titanium is 0.60 or less is obtained by reacting the following compound (a1) with the following compound (b1) at a hydroxyl group/magnesium molar ratio of 1.0 or more, reacting the reaction mixture with the following compound (c1) at a halogen/magnesium molar ratio of 0.20 or more, reacting the resultant reaction mixture with the following compounds (d1) and (e) at a temperature of 120.degree. C. or higher but 150.degree. C. or lower, washing the reaction mixture with an inert solvent, reacting the reaction mixture with the following compound (e) again at the above temperature and washing the reaction mixture with an inert solvent, whereby there can be provided the solid catalyst component for olefin polymerization and a catalyst for olefin polymerization which have high polymerization activity and give an olefin polymer having a less residual Cl content and being excellent in stereoregularity and powder form and a process for producing an olefin polymer, (a1) an oxide of at least one element that is selected from Group II to Group IV elements and which supports an alcohol-free halogen-containing magnesium compound, (b1) an alcohol, (c1) a halogen-containing silicon compound, (d1) an electron-donating compound, and (e) a halogen-containing titanium compound.