A polypropylene composition capable of producing molded products having superior stiffness, impact resistance, transparency, resistance to whitening on impact on bending and luster is provided, which com­position has (i) a styrene-ethylene·butylene-styrene block copolymer or a styrene-ethylene·propylene block copolymer each in 5 to 30% by weight based on the weight of the composition, blended with a highly crystalline propylene homopolymer (A) having a relationship between its isotactic pentad ratio (P) and melt flow rate (MFR) represented by an expression of
    1.00 ≧ P ≧ 0.015 log MFR + 0.955;
(ii) a styrene-ethylene·butylene-styrene block copolymer or a styrene-ethylene·propylene block copolymer each in 5 to 30% by weight based on the weight of the composition and an ethylene-propylene copolymer rubber or a poly­ethylene each in 15% by weight based thereon, blended with the above (A), the blending proportion of (A) being 60% by weight or more based on the weight of the compo­sition; or (iii) a styrene-ethylene·butylene-styrene block copolymer or a styrene-ethylene·propylene block copolymer, each in 5 to 30% by weight based on the weight of the composition, an ethylene-propylene rubber and polyethylene each in 15% by weight or less based thereon, blended with the above (A), the blending proportion of (A) being 60% by weight or more based thereon.