An object of the present invention is to provide an adhesive resin composition which displays excellent adhesive strength on bonding to a barrier material, during initial adhesion, durable adhesion, and even after soak in fuel oil, and which also has excellent moldability. Furthermore, another object of the present is to provide an adhesive resin composition which when recycled, displays good compatible in a regrind layer with polyethylene resins and barrier materials such as saponified products of ethylene-vinyl acetate copolymers or polyamide based resins, and which is consequently capable of suppressing deterioration in the low temperature impact resistance of a multi-layer vessel containing a regrind layer. In order to achieve these objects, the present invention provides an adhesive resin composition (C) comprising (A) 100 to 5% by mass of a modified polyethylene in which an unsaturated carboxylic acid and/or an unsaturated carboxylic acid derivative unit is grafted to a high molecular weight polyethylene with a melt flow rate (MFR: temperature 190.degree. C., loading 2.16 kg) of 0.1 to 2.0 g/10 minutes, and a density of 0.91 to 0.96 g/cm.sup.3, and (B) 0 to 95% by mass of an unmodified polyethylene with a melt flow rate (MFR: temperature 190.degree. C., loading 2.16 kg) of 0.1 to 20 g/10 minutes, and a density of 0.86 to 0.96 g/cm.sup.3, wherein the density of the adhesive resin composition (C) is 0.925 to 0.940 g/cm.sup.3, the content of the unsaturated carboxylic acid and/or unsaturated carboxylic acid derivative unit incorporated therein is at least 0.09% by mass, and the melt flow rate (MFR: temperature 190.degree. C., loading 2.16 kg) is from 0.1 to 2 g/10 minutes.