Pricing variance swaps under stochastic volatility with discretely-sampled realized variance has been a hot subject pursued recently; quite a few papers have already been published (Zhu and Lian (2009, 2011, [11,4]); Swishchuk and Li (2011) ). In this paper, we present a simplified approach to price discretely-sampled variance swaps. Compared with the approach presented by Zhu and Lian (2011) , an important feature of our approach is that there is no need for the introduction of a new state variable and the utilization of the generalized Fourier transform. This has significantly simplified the solution procedure and will thus enable researchers to view this type of problems from a different angle. © 2011 Elsevier Ltd. All rights reserved.