We present a GPU-based computation for simulating the synthetic aperture radar (SAR) image of the complex target. To be more realistic, we included the multiple scattering field and antenna pattern tracking in producing the SAR echo signal for both Stripmap and Spotlight modes. Of the signal chains, the computation of the backscattering field is the most computationally intensive. To resolve the issue, we implement a computation parallelization for SAR echo signal generation. By profiling, the overall processing was identified to find which is the heavy loading stage. To further accommodate the hardware structure, we made extensive modifications in the CUDA kernel function. As a result, the computation efficiency is much improved, with over 224 times the speed up. The computation complexity by comparing the CPU and GPU computations was provided. We validated the proposed simulation algorithm using canonical targets, including a perfectly electric conductor (PEC), dielectric spheres, and rotated/unrotated dihedral corner reflectors. Additionally, the targets can be a multi-layered dielectric coating or a layered medium. The latter case aimed to evaluate the polarimetric response quantitively. Then, we simulated a complex target with various poses relative to the SAR imaging geometry. We show that the simulated images have high fidelity in geometric and radiometric specifications. The decomposition of images from individual scattering bounce offers valuable exploitation of the scattering mechanisms responsible for imaging certain target features.