In this paper, we propose a peak-weighted cepstral lifter (PWL) for enhancing the spectral peaks of an all-pole model spectrum in the cepstral domain. The design parameter of the PWL is the degree of pole enhancement or pole shifting toward the unit circle. The optimal pole shifting factor is chosen by considering the sensitivity to spectral resonance peaks, the variability of cepstral variances, and the recognition accuracy. Next, we generalize the PWL so that the optimal shifting factor is adaptively determined in frame-by-frame basis. Compared with other cepstral lifters, a speech recognizer employing the frame-adaptive PWL provides better recognition performance.