Combining the interpolation function, which has the delta function property and is constructed on the basis of radial basis functions and polynomial functions, using the local boundary integral equation method (LBIE), the local boundary integral equation method based on radial basis functions is presented for potential problem in this paper. The corresponding discrete equations are obtained. Comparing with the other meshless boundary integral equation methods, the present method has simpler numerical procedures, lower computation cost and higher accuracy. In addition, the essential boundary conditions can be implemented directly. Some numerical results to show the efficiency of the present method are given.