In order to improve the performance of general sidelobe canceller （GSC） based speech enhancement, a leakage constraints decision feedback generalized sidelobe canceller（LCDF-GSC） algorithm is proposed. The method adopts DF-GSC against signal mismatch, and introduces a leakage factor in the cost function to deal with the speech leakage problem which is caused by the part of the speech signal in the noise reference signal. Simulation results show that although the signal-to-noise ratio （SNR） of the speech signal through LCDF-GSC is slightly less than that of DF-GSC, the IS measurements show that the distortion of the former is less than that of the latter. MOS （mean opinion score） scores also indicate that the LCDF-GSC algorithm is better than DF- GSC and the Weiner filter algorithm,
