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We present a scheme to simulate SH-wave propagation in a whole-Earth model with arbitrary lateral heterogeneities employing the Fourier pseudospectral method. Wave equations are defined in two-dimensional cylindrical coordinates and the model is taken through a great circle of the Earth. Spatial derivatives in the wave equations are calculated in the wavenumber domain by multiplication, and the transformation between spatial and wavenumber domains is performed via fast Fourier transformation. Because of the high accuracy and high speed of the Fourier pseudospectral method, the scheme enables us to calculate a short-wavelength global SH-wavefield with accurate waveforms and arrival times for models with heterogeneities that can be approximated as azimuthally symmetric. Comparing with two-dimensional simulation methods based on an axisymmetric model, implementing the seismic source in the present scheme is more convenient. We calculated the global SH-wavefield for the preliminary reference Earth model to identify the generation, reflection and refraction of various seismic phases propagating in the Earth. Applications to a heterogeneous global model with low-velocity perturbation above the core-mantle boundary were conducted to analyze the effect of lateral heterogeneity on global SH-wave propagation.