A catalyst for polymerization of olefins formed from (A) a solid catalyst component containing magnesium, titanium, halogen, and an electron donor compound, (B) an organoaluminum compound shown by the formula, R6pAlQ3-p, and (C) an aminosilane compound shown by the formula, R3nSi(NR4R5)4-n; and a process for producing a catalyst for polymerization of olefins in the presence of the catalyst are provided. A novel aminosilane compound, a catalyst component for polymerization of olefins having a high catalytic activity, capable of producing polymers with high stereoregularity in a high yield, and exhibiting an excellent hydrogen response, a catalyst, and a process for producing olefin polymers using the catalyst are provided.