For iterative calculations of synthetic seismograms with limited computer resources, a fast and accurate modeling method is needed. Axisymmetric modeling has often been used in global seismology to restrict computational time and storage. This approach can correctly model 3-D geometrical spreading effects with computational times comparable to 2-D methods, but cannot treat asymmetric structures about the source axis. To overcome this problem, a new approach is proposed for seismic wave propagation in a 2-D slice through a global Earth model with lateral heterogeneity. The elastodynamic equation for spherical coordinates is not solved in the conventional spherical domain but instead in the quasi-spherical domain using the finite-difference method. The validity and efficiency of this technique is illustrated with numerical examples including subduction zone structures.