To provide an adhesive ethylene-based polymer composition easily exhibiting an excellent bonding property and maintaining mechanical properties such as tensile strength, etc., well, and a method for bonding with cross-linking, an ethylene-based polymer composite material and a fiber-reinforced belt using the same.

This adhesive ethylene-based polymer composition contains (A) an ethylene-based polymer, (B) a cross-linking agent consisting of a peroxide having cross-linking activity and (C) a stickiness-imparting agent consisting of a peroxide other than the above mentioned peroxide and having hydroperoxy group. The content of the (B) cross-linking agent is 0.6-20 pts.mass and the content of the (C) stickiness-imparting agent is 0.4-15 pts.mass based on the (A) 100 pts.mass ethylene-based polymer, and the content of the (C) stickiness-imparting agent based on the (B) 100 pts.mass cross-linking agent is 30-80 pts.mass. As the peroxide of the (B) cross-linking agent, a dialkylperoxide is preferable, and as the peroxide of the (C) stickiness-imparting agent, a hydroperoxide is preferable.