This paper presents a new speech enhancement method. It consists of two processing steps. The first processing step is the estimation of speech spectrum from noisy speech, for which a VQ method is adopted that uses two LPC cepstrum codebooks. One of the codebooks is generated from a clean speech database and the second one corresponds to that of noisy speech. Each entry of the noisy speech codebook corresponds to one of the entries of the clean speech codebook. Extracted VQ code of noisy speech is transformed into a clean one using the correspondence between the noisy and the clean codebooks. This method, based on the pairing of two codebooks, makes it possible to recover attenuated or lost formants. The second processing step is to restore the speech waveform. A modified Wiener filtering has been adopted. Also developed is a VQ method of noisy speech using only the clean speech codebook. The estimated LPC cepstrum coefficients of noisy speech are transformed into clean ones using an experimentally determined mathematical model. The noisy speech codebook depends on the signal-to-noise ratio and noise characteristics. The second method can be applied to any noise conditions. Experimental results showed the effectiveness of the proposed method.