In this paper, a novel boundary element method (BEM) is proposed, which is based on the scaling functions of B-spline wavelet on the interval (BSWI). The conventional interpolation functions are replaced by scaling function to develop the basic functions and BSWI elements. Different from other wavelet methods is that we are supposed to transform the coefficient matrix from wavelet space to physical space through a transformation matrix, which is an extremely necessary tool to allocate nodes with freedom, but there is an additional condition that we have to guarantee its non-singularity. At last, the numerical example verifies that comparing with traditional boundary element method, the BSWI elements have a desirable performance, such as higher precision and fewer elements. Furthermore, it effectively enriches the wavelet-based boundary element method library.