We have proposed a noise reduction method based on a noise reconstruction system (NRS). The NRS uses a linear prediction error filter (LPEF) and a noise reconstruction filter (NRF) which estimates background noise by system identification. In case a fixed step size for updating tap coefficients of the NRF is used, it is difficult to reduce background noise while maintaining the high quality of enhanced speech. In order to solve the problem, a variable step size is proposed. It makes use of cross-correlation between an input signal and an enhanced speech signal. In a speech section, a variable step size becomes small so as not to estimate speech, on the other hand, large to track the background noise in a non-speech section.