Poly(2-acrylamido-2-methyl-1-propanesulfonic acid) (poly(AMPS)) bearing a sulfo group was grafted onto a polyurethane sponge by an argon atmospheric-pressure plasma treatment and subsequent graft polymerization. Thus, a novel poly(AMPS)-grafted polyurethane sponge was developed as a heterogeneous acid catalyst for organic synthesis. The average grafting amount was 0.0277 kg-polymer/kg-substrate. The surface properties of the polyurethane sponge changed considerably, from hydrophobic to hydrophilic. The poly(AMPS)-grafted sponge successfully catalyzed the acetalization of glycerol with acetone to produce the desired solketal. The reaction rate was analyzed using a pseudo-first-order kinetic model, and the apparent reaction rate constant, k, and apparent activation energy were determined. The k value for the poly(AMPS)-grafted sponge was one order of magnitude larger than that for the EDGA-co-AMPS gel (EDGA: ethoxy diethyleneglycol acrylate). The poly(AMPS)-grafted sponge with interconnected submillimeter-sized macropores and high porosity (98%) exhibits excellent diffusional permeability. In addition, the structural features of the sponge provide advantages such as a negligible pressure drop and easy handling during the reaction process. This study provides a strategy for the use of polymers grafted onto sponges as catalysts.