PURPOSE: To produce PP having an excellent low-temperature impact strength and a high crystallization velocity, by mixing a specitied α-olefin/ethylene random copolymer with PP, adding an org. peroxide and a crosslinking aid there to and heat-treating the mixture.

CONSTITUTION: 0.01W1pt.wt. org. peroxide such as dicumyl peroxide and 0.001W 10pts.wt. crosslinking aid such as divinylbenene are mixed with 100pts.wt. compsn. consisting of 55W95pts.wt. PP (A), 1W40pts.wt. α-olefin/ethylene random copolymer (B), pref. one having an α-olefin (e.g. propylene) content of 10W70% and triad isotacticity of less than 0.7 and 1W35pts.wt. PE (C). The mixture is heat-treated at 180W350°C. By adding the copolymer B to PP and further adding the org. peroxide and the crosslinking aid thereto, PP having excellent low-temperature impact strength and a high crystallization velocity can be obtd. without detriment to rigidity, inherent to PP.