The present invention relates to an adhesive polyethylene composition comprising (A) from 60 to 90 wt% of a non-elastomeric polyethylene; (B) from 9.0 to 38 wt% of an ethylene based elastomer being a copolymer of ethylene and alpha-olefin comonomer units having from 4 to 12 carbon atoms; wherein onto component (A) or components (A) and (B) an acid grafting agent (C) has been grafted in an amount of from 0.01 to 3.0 wt%, all based on the total weight of the adhesive polyethylene composition, a multi-layer structure comprising said adhesive polyethylene composition and the use of said adhesive polyethylene composition for the production of a multi-layer structure.