This paper presents a technique for estimating HMM model parameters for noisy speech from given clean speech HMM and noise HMM. The model parameters are estimated by approximating the non-linear function governing the relationship between speech and noise, by a Lagrange polynomial, and thus enabling the distribution of corrupted speech parameters to have a closed form. The method is computationally efficient, and the experimental results showed significant improvement in recognition performance of noisy speech with this approach. Typically, word accuracy increased from 9.2% with clean model to 82.8% with the model composed by the proposed method as compared to 45.4% with the model composed by PMC Log-normal approximation, on an isolated word recognition task for exhibition hall noise added at 10 dB SNR.