As a powerful and flexible processor, the Graphic Processing Unit (GPU) can offer a great faculty in solving many high-performance computing applications. Sweep3D, which simulates a single group time-independent discrete ordinates (Sn) neutron transport deterministically on 3D Cartesian geometry space, represents the key part of a real ASCI application. The wavefront process for parallel computation in Sweep3D limits the concurrent threads on the GPU. In this paper, we present multi-dimensional optimization methods for Sweep3D, which can be efficiently implemented on the finegrained parallel architecture of the GPU. Our results show that the overall performance of Sweep3D on the CPU-GPU hybrid platform can be improved up to 4.38 times as compared to the CPU-based implementation.