For curve skeleton extraction algorithm, in order to improve the efficiency of potential field computation and save the time of extraction process, we presented a parallel potential field skeleton extraction method to reduce the time complexity, which was suitable for implementation on GPU, and then improved it by using constant memory and shared memory which was unique in CUDA. In order to achieve the highest GPU occupancy and the best speedups, we discussed how to assign threads according to the property of program and graphics device. The implementation was tested on several complex 3D models in CUDA framework. The results showed that our method had excellent performance especially on large data scale. When processing the volume data with the scale of 256×256×487, this improved method achieved speedups of 18x.