Pseudospectral method is an efficient and high-accuracy numerical modeling technique that has been applied to the simulation of seismic wavefields in realistic models with complex structures such as sedimentary basin. However, if the sedimentary layers are included in the model, high velocity contrasts arise because of the very low S-wave velocities of the sediments as compared with the bedrock. The grid spacing then has to be very small, which leads to spatial oversampling in regions with higher velocities. As a result, we also have to use very small time interval for time marching, so that the computation requires much CPU time. A treatment of this problem is use of a multidomain approach that can employ different grid spacings in different regions, i.e. "discontinuous grid". In this study, we propose a scheme for the Fourier pseudospectral method using discontinuous grid, which uses an interpolation by the FFT. This scheme can reduce the computation time and the required computer memory as compared with the conventional one. The accuracy and efficiency of this approach are demonstrated in the present paper through examples of 2-D elastic wave modeling.