To obtain the subject composition containing a specific crystalline propylene-α-olefin copolymer, a specific low molecular weight polyethylene and a specific block copolymer at a specific ratio, excellent in transparency without whitening by sterilization treatment and useful for food containers, etc.

This olefin polymer composition contains (A) 98.8-78.5wt.% crystalline propylene-α-olefin copolymer having 120-150°C melting point of crystal, (B) 0.2-1.5wt.% low molecular polyethylene having 0.91-0.940 density and 2000 to 15000 weight average molecular weight and (C) 1-20wt.% hydrogenated diene-based block copolymer obtained by saturating ≥80% double bond of a conjugated diene part of a block copolymer comprising an aromatic vinyl compound polymerization part and a conjugated diene polymerization part by hydrogenation.