Based on CUDA Fortran for compressible turbulence simulations, a finite volume computational fluid dynamics solver on the GPU(Graphical Processing Unit） was developed. The solver was implemented with an AUSMPW+ scheme for the spatial dispersion, the k-ω SST model for turbulence model, and MPI communication for parallel computing. Some optimization strategies for fluxes computation and multi-GPU parallel algorithms for overlap of PCIe data transfer and MPI communication with GPU computation have been discussed for the latest generation GPU architecture. Several test cases, such as a supersonic inlet and a space shuttle were chosen to demonstrate the acceleration performance of GPU on large-scale grid size. Results show that when using a NVIDIA GTX Titan Black GPU, the computational expense can be reduced by 107～125 times than using a single core of an Intel Xeon E5-2670 CPU. Fast computing for a complex configuration with 0.134 billion grid sizes has been achieved by using 4 GPUs and the parallel efficiency is 91.6%.