When the particle filter has too many particles, the computational cost increases and the sequential algorithms become inefficient in terms of the execution time. Recent developments in the graphics processing unit technology offer promising solutions for the speedup of the particle filter. In this study, Sampling Importance Resampling (SIR) particle filter method is implemented on the graphics processing unit. The speedup results are compared with results of the sequential and parallel implementations of the SIR particle filter on the central processing unit. The results show that the solution in the graphics processing unit obtains about 12 times speedup over the sequential algorithm. Furthermore, the importance of the parallel solution of the resampling step in the SIR particle filter is pointed out.