In this paper, we generalize relations between clean and noisy speech signal using vector Taylor series (VTS) expansion for noise-robust speech recognition. We use it for both the noisy data compensation and hidden Markov model (HMM) parameter adaptation, and apply it for the cepstral domain directly, while Moreno used it to estimate the log-spectral parameters. Also, we develop a detailed procedure to estimate environmental variables in the cepstral domain using the expectation and maximization (EM) algorithms based on the maximum likelihood (ML) sense. To evaluate the developed method, we conduct speaker-independent isolated word and continuous speech recognition experiments. White Gaussian and driving car noises added to clean speech at various SNR are used as disturbing sources. Using only noise statistics obtained from three frames of silence and noisy speech to be recognized, we achieve significant performance improvement. Especially, HMM parameter adaptation with VTS is more effective than the parallel model combination (PMC) based on the log-normal assumption.