This paper proposes and adaptive nonlinear equalizer based on Volterra Series along with M-band wavelet transform(M-DWT). The proposed wavelet transform-domain approach leads to diagonalization of the input vector auto-correlation matrix, which yields clustering its eigenvalue spread around one, and improving the convergence rate of the corresponding transform-domain LMS algorithm. In particular, the proposed adaptive Volterra equalizer is employed to compensate for the output distortion produced by a weakly nonlinear system. Finally, some simulation results obtained by using a TWT amplifier model are provide to demonstrated the converging performance of the proposed approach.