A graft copolymer composition which gives a molding retaining a satisfactory appearance over long and from which a molding less apt to be worn, marred, or bent can be easily molded. The graft copolymer composition comprises a graft copolymer of a multiphase structure as the main component and a lubricant comprising a fatty acid amide or alkylene oxide derivative. The graft copolymer comprises olefin polymer segments (a) and vinyl polymer segments (b), wherein particles of the segments of one polymer are dispersed in the segments of the other polymer. The particles have a diameter of 0.001 to 10 µm. The vinyl polymer segments (b) are formed from a polar vinyl monomer.