A novel cation exchange membrane based on a styrene-hydroxy ethyl acrylate-lauryl methacrylate terpolymer (St-HEA-LMA) was prepared. Sulfonic groups were introduced to the membrane structure with sulfuric acid as the sulfonating agent and silver sulfate as the initiator. Sulfonated St-HEA-LMA terpolymer membranes were characterized by Fourier-transform infrared (FTIR) spectroscopy and atomic force microscopy (AFM), as well as by determining the degree of sulfonation (DS), ion-exchange capacity (IEC), swelling ratio and electrical resistance of the membranes. The presence of sulfonic groups in the sulfonated St-HEA-LMA terpolymer was confirmed by FTIR, and the resulting membrane exhibited an ion-exchange capacity of 2.13 meq/g and an electrical resistance of 1.17 $Omega{cdot}cm^2$. The swelling ratio of the prepared membranes increased with increasing degree of sulfonation, and the tensile strength decreased with increasing degree of sulfonation at a reaction temperature of $30^{circ}C$. The phase images obtained by AFM clearly showed an increase in roughness with increasing DS. Considering the mechanical properties, the sulfonated St-HEA-LMA terpolymer obtained at a sulfonation reaction temperature of $20^{circ}C$ was suitable for ion-exchange membrane applications.