We propose a new noise reduction method for speech signals using running spectrum filtering (RSF) and new musical noise reduction. RSF, which uses FIR filtering, is realized in the modulation frequency domain and it can eliminate noise components effectively using running spectra of speech. Since some musical noise happens on RSF, a new post processing is also introduced for musical noise reduction. The report shows that the proposed method is well applied for speech enhancement. It also indicates that segmental SNR is improved and audibility evaluation shows a higher score than conventional processing.