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In this letter, implementation of the finite-difference time domain (FDTD)-compatible Green's function on a graphics processing unit (GPU) is presented. Recently, closed-form expression for this discrete Green's function (DGF) was derived, which facilitates its applications in the FDTD simulations of radiation and scattering problems. Unfortunately, implementation of the new DGF formula in software requires a multiple precision arithmetic and may cause long runtimes. Therefore, we propose an acceleration of the DGF computations on a GPU employing the multiple precision arithmetic and the CUDA technology. We have achieved sixfold speedup relative to the reference DGF code executed on a multicore central processing unit. Results indicate that GPUs also represent an inexpensive source of computational power for accelerated DGF computations requiring the multiple precision arithmetic.