In this paper, the dielectric properties of water-dimethylsulfoxide (DMSO) mixtures with different mole ratios have been investigated in the range of 1 GHz to 40 GHz at 298 K by using a molecular dynamics (MD) simulation. Only one dielectric loss peak was observed in the frequency range and the relaxation in these mixtures can be described by a single relaxation time of the Davidson-Cole. It was observed that within experimental error the dielectric relaxation can be described by the Debye-like model (beta approximate to 1, S. M. Puranik, et al. J. Chem. Soc. Faraday Trans. 1992, 88, 433-435). In general, the results are very consistent with the experimental measurements.