A polyolefin composition comprises 100 parts by weight of a polyolefine which has been produced with use of a Ziegler catalyst and has a part or residue of the catalyst left therein, 0.005 to 1 part by weight of a phenol compound having the formula (I) and 0.005 to 1 part by weight of an organic phosphite compound having the formula (II). ##STR1## in which R is a residue group of an alcohol being monohydric, dihydric, trihydric or terahydric, R1 is methyl or tert.-butyl, R2 is an alkyl, --CH2CH2COOR3 or --COOR3, R3 being an alkyl, an aryl or an alkylaryl, and n is a number of 1 to 4.