The present invention herein provides a plastic multi-layer structure which comprises an oxygen-barrier layer (A-1), an oxygen absorptive layer (B), and a thermoplastic resin layer (C) containing a high silica type zeolite material having a silica/alumina ratio of not less than 80; and a packaging material such as bottles for accommodating foods, for instance, a beverage and medical and pharmaceutical products. The plastic multi-layer structure possesses oxidation-barrier characteristics and the structure would permit the considerable reduction of the quantity of the oxidation by-products generated from the structure, even when used under a high humidity atmosphere.