We have investigated a noise reduction method based on a linear prediction error filter (LPEF) and system identification. Background noise is estimated by system identification. In the case of using a fixed step size with which tap coefficients of an adaptive filter is updated, it is difficult to reduce background noise while maintaining the high quality of enhanced speech. Therefore, a variable step size is proposed. In a speech section, a small step size is used so as not to estimate speech. On the other hand, a large step size is used to track background noise in a non-speech section.