An acid-functionalized polyolefin material that can be used as an acid catalyst in a wide range of acid-promoted chemical reactions, wherein the acid-functionalized polyolefin material includes a polyolefin backbone on which acid groups are appended. Also described is a method for the preparation of the acid catalyst in which a precursor polyolefin is subjected to ionizing radiation (e.g., electron beam irradiation) of sufficient power and the irradiated precursor polyolefin reacted with at least one vinyl monomer having an acid group thereon. Further described is a method for conducting an acid-promoted chemical reaction, wherein an acid-reactive organic precursor is contacted in liquid form with a solid heterogeneous acid catalyst comprising a polyolefin backbone of at least 1 micron in one dimension and having carboxylic acid groups and either sulfonic acid or phosphonic acid groups appended thereto.