In this paper, the pricing problems of variance swaps with discrete sampling times are studied, where the volatility of underlying assets follows a mean-reverting Gaussian (MRG in short) process, and the instantaneous interest rate is described by classical Vasicek model. By using measure transformation, Feynman-Kac formula and Fourier transform algorithm, a closedform analytic pricing formula for variance swaps with the actual-return realized variance is presented.