Refereed/Peer-reviewed Path planning of mobile robot has become a research hotspot in the fields of automatic control, computer and artificial intelligence. The sampling-based method is one of the most popular methods for path planning, among which BIT*(Batch Informed Trees), a variant of RRT, is a typical one. However, it has to traverse the space to find the first path, and will generate some redundant points which bringing a lot of redundant angles. As BIT* is not optimal and the convergence is not fast enough, a new sampling-based method, GSGC, is proposed to overcome these shortcomings in this paper. It adds an alterable guided sampling function to increase sampling efficiency. To remove redundant points, a gradual cutting function is presented to reduce the length of path and improve processing efficiency. During pruning, the elliptical area is shrunk to reduce the sampling space which improves the performance. The experimental results show that the GSGC can spend less time to get an optimal solution with faster convergence than BIT* and RRT*.