This paper proposes a novel HMM adaptation algorithm for robust automatic speech recognition (ASR) system in noisy environments. The HMM adaptation using vector Taylor series (VTS) significantly improves the ASR performance in noisy environments. Recently, the power normalized cepstral coefficient (PNCC) that replaces a logarithmic mapping function with a power mapping function has been proposed and it is proved that the replacement of the mapping function is robust to additive noise. In this paper, we extend the VTS based approach to the cepstral coefficients obtained by using a power mapping function instead of a logarithmic mapping function. Experimental results indicate that HMM adaptation in the cepstrum obtained by using a power mapping function improves the ASR performance comparing the VTS based conventional approach for mel-frequency cepstral coefficients (MFCCs).