The invention pertains to a process for producing a cross-linked polyolefin foam in a continuous process using standard processing equipment without using a moisture cross-linking step after processing. In this method, a vinyl functional silane compound is melt grafted onto a low density polyethylene in the presence of a free radical generator. The resulting silane grafted polyethylene resin is mixed and melted with a blowing agent in a continuous process in the presence of water to form a vinyl functional silane foam.