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The particle-in-cell (PIC) algorithm for the simulation of charged-particle kinetics in plasmas is a very resource consuming method, and high-performance parallel computing is required for practical problems. Graphics processing units (GPUs) are powerful low-cost parallel systems that can be used for intensive computations. We have developed a PIC Monte Carlo collision (MCC) model of a low temperature magnetized plasma using GPUs. We describe how each part of the PIC MCC model is implemented on the GPU and show how particles are dynamically managed. The computational cost of the PIC MCC model on the GPU is compared with a standard PIC MCC model running on a single central processing unit (CPU). We show that speedup can reach from 10 to 20 times compared with a sequential code running on a CPU, depending on the number of cells and particles considered. The results are illustrated with the example of plasma transport across a magnetic filter similar to that of a negative-ion source for the neutral beam injector of fusion devices.