In order to reduce the economic loss caused by well leakage and the lag of drilling progress, it is very important to use plugging materials reasonably and effectively. Expandable polymer materials can better fill cracks and holes of different sizes by absorbing water expansion and deforming. In this article, an expandable polymer plugging agent (PSMAN) was prepared by soap‐free emulsion polymerization using methyl methacrylate (MMA), styrene (St), 2‐acrylamide‐2‐methylpropanesulfonic acid (AMPS) as reaction monomers, N‐hydroxymethyl acrylamide (NMA) as a cross‐linking agent, and ammonium persulfate (APS) as initiator. The optimal synthesis conditions were determined by designing the orthogonal experiments, and the various properties of the materials were tested and evaluated. The experimental results show that PSMAN has good high temperature resistance, spherical structure, and median particle size of 15.099 μm, and the water absorption rate of room temperature at 24 h reaches 37.8 g/g, and pressure bearing capacity can reach 5 MPa. The addition of polymer to water‐based drilling fluid can increase the viscosity of drilling fluid and improve the rheological properties of drilling fluid by a small amount. Under normal temperature and medium pressure, the polymer can form a dense film on the surface of the mud cake, thereby reducing the filtration of drilling fluid and effectively improving the stability of the wellbore.