To provide an olefin polymer composition which is suitable as an easy-peelable sealant, particularly, is suitable as a lid-material sealant of a container made from polypropylene, is excellent in a sealing property, a low-temperature heat-sealing property, an easy-peelable property and an appearance of a peeled portion, shows a low temperature-dependent property of heat-sealing strength, and has oil resistance.

The olefin polymer composition is obtained by compounding at a ratio of an ethylene/unsaturated ester copolymer (E-1) of 30-98 pts.wt. containing the unsaturated ester of 3-20 wt.%, an ethylene/unsaturated ester copolymer (E-2) of 1-40 pts.wt. containing the unsaturated ester of 25-50 wt.%, a wax (F) of 1-30 pts.wt. and a tackifying resin (D) of 0-30 pts.wt.