A new gamma-ray stabilizer comprising a combination of 100 parts by weight of a benzyl compound (A) having a specific chemical structure and 0.01 to 10 parts by weight of a pentaerythritol phosphorous ester (B) having a spirocyclic structure. Said stabilizer is preferably blended in such a manner that said (A) is contained in an amount of 0.01 to 10 parts by weight based on 100 parts by weight of a thermoplastic polymer (polycarbonate or the like), and said (B) is contained in an amount of 0.01 to 1 part by weight based on 100 parts by weight of said (A). When the thermoplastic polymer is subjected to gamma-ray irradiation, said stabilizer can efficiently protect the thermoplastic polymer from the deterioration of physical properties and yellowing; and on molding processing, the stabilizer-added polymer is suffered from little color tone deterioration and has excellent color tone, and at the same time, the polymer is scarcely suffered from molecular weight decrease on molding, and exhibits excellent thermal stability, moldability or the like. The thermoplastic polymer (especially polycarbonate) composition containing said stabilizer thus obtained is suitable for medical apparatus and medical material uses, especially a jacket case for an artificial dialyzer.