This paper proposes a blind multi-user detection algorithm under the fading channels in the existence of impulse noise based on signal sub-space estimation. Usually the traditional filtering algorithms adapt training data sequences and need more knowledge about the spreading waveform, which may delay the desired user. This algorithm adapts RLS filter that can estimate the coefficients only using the signature waveform. In addition, a new suppressive factor is induced to suppress the amplitude of the impulse and improve the convergence speed. Simulation results show that new RLS algorithm is more robust against consecutive impulse noise and have better convergence ability than conventional RLS.