An adaptive system is a well-known method for removing noise from noise-corrupted speech. In this paper, we perform a least mean square (LMS) based on wavelet adaptive algorithm. It establishes the faster convergence rate of as compared to time domain because of eigenvalue distribution width. And this paper provides the basic tool required for the FIR algorithm whose algorithm reduces the arithmetic complexity. We consider a new fast short-length running FIR structure in discrete wavelet adaptive algorithm. We compare FIR algorithm and short-length fast running FIR algorithm (SFIR) to the proposed fast short-length running FIR algorithm(FSFIR) for arithmetic complexities.