To obtain a crystalline propylene block copolymer composition excellent in flowaility at the time of molding and, in addition, the balance of properties.

This crystalline propylene block copolymer comoposition comprises (A) 40-90 wt.% crystalline propylene block copolymer composed of propylene homopolymer moieties (Fp) and ethylene-propylene random copolymer moieties (Fc) and having an ethylene content of 1-10 wt.% and a melt flow rate(MFR), measured at 230°C under a load of 2,160g, of 20-100 g/10 min, (B) 5-35 wt.% elastomeric polymer, and (C) 5-25 wt.% inorganic filler, the Fp containing 20-50 wt.% low molecular propylene hompolymers (Fh) with an MFR 400-1,000 g/10 min and having an average MFR of 100-350 g/10 min and an isotactic pentad rtio, measured by 13C-NMR, of not less than 98% and the Fc having an intrinsic viscosity [η], measured at 135°C in decahydronaphthalene, of not less than 7 dl/g.