Free-radical polymerization in solution was used to synthesize a terpolymer consisting of acrylamide, 2-acrylamido-2-methylpropanesulfonic acid, and styrene sulfonate. Drilling fluids based on the terpolymer were prepared for use in high-temperature and high-pressure wells. The rheological properties of the drilling fluids based on the terpolymer were analyzed by the regression method. We found that the rheological properties of the drilling fluids at high temperature and high pressure can be described by the Casson model. A mathematical model is proposed for predicting the downhole viscosity of drilling fluids containing the terpolymer at high temperature and high pressure.