Starting from a nonpolarizable rigid molecular model for DMSO, a polarizable rigid model for DMSO in the liquid phase is proposed. The molecular polarizability is represented by a charge-on-spring (COS) inducible dipole at the sulfur atom and its polarization is damped for large values of the electric field strength. Some parameters of the model, the partial charge distribution, the polarizability, the value of the electric field at which damping sets in, were varied, and the overall depth and repulsion strength of the Lennard-Jones interactions were scaled with the aim of reproducing the experimental values for the molecular dipole moment, the density, heat of vaporization, and static dielectric constant of liquid DMSO at ambient temperature and pressure. The polarizable DMSO/D model well reproduces the experimental data, such as excess free energy, surface tension, translational, and rotational diffusion, for liquid DMSO. The model is further tested in mixtures with polarizable water models and in mixtures with nonpolarizable DMSO. The latter results suggest that it could serve as model for polarizable cosolvent in aqueous solutions.