The multi-dimensional neutron transport process is simulated by using the lattice Boltzmann method(LBM) with strong localization. Meanwhile, to improve the computational speed of LBM, the Graphics Processing Unit(GPU) acceleration is applied to speed up the LBM calculation in parallel. The numerical solutions for typical neutron transport cases show that the LBM can simulate the neutron transport problem accurately and the GPU acceleration can efficiently improve the computational speed of the LBM. The combination of these two techniques can realize the efficient and accurate neutron transport calculation.