Abstract: A novel weighted wavelet is constructed by using the subdivision scheme and recursive average interpolated method. Its characteristics is respectively proved to be compact supported, smooth, vanishing moment, and orthogonal. Compared with the common wavelet by the Fourier transform, the decay of weighted wavelet coefficient is faster than that of the common wavelet. Furthermore, the method is simple and easily applied. Its computational complexity is greatly reduced. The simulation demonstrate that the weighted wavelet is sufficiently smooth even though the weighted function has a large jump, and that it can approximate functions exactly and the approximated convergence is faster.