Noise-resistant speech HMMs are composed by: recording noise in the environment of utterance (S.sub.1); preparing HMMs of the noise (S.sub.2); transforming the output probability distribution of each of the noise HMMs and speech HMMs prepared from speech unaffected by noise and multiplicative distortion to a linear spectral domain (S.sub.31); multiplying the speech HMM distribution in the linear spectral domain by a multiplicative distortion W that is an unknown variable (S.sub.321); convoluting the multiplied value and the noise HMM distribution in the linear spectral domain (S.sub.322); inversely transforming the convoluted value to the original domain of the speech HMM (S.sub.33) to compose incomplete noise-resistant speech HMMs each containing multiplicative distortion as an unknown variable (S.sub.3); calculating the likelihoods of the incomplete noise-resistant speech HMMs for input speech and estimating the multiplicative distortion of that one of the incomplete noise-resistant HMMs which has the maximum likelihood (S.sub.4); and substituting the estimated value into the incomplete noise-resistant speech HMMs (S.sub.5).