The increasing of experimental observations' accuracy and model complexity of the heliospheric cosmic rays modulation requires the development of a new class of numerical solvers. In this work, we present a GPU-accelerated code for solving the Parker propagation equation in the heliosphere using a stochastic differential equation (SDE) approach. The proposed method uses the CUDA programming language developed for NVIDIA GPUs. Our approach achieves a speedup of the orders of ~10-40, depending on the number of quasi-particle simulated, compared to the previous CPU implementation. This allows us to efficiently solve the transport equation for the modulated spectra of charged particles in the heliosphere, opening the field for deeper studies and making the realized simulations available for general-purpose studies. We demonstrate the accuracy and efficiency of our method through numerical experiments on a realistic model of the heliosphere.