Recently, the multi-model based speech recognizer has been used quite successfully for noisy speech recognition. For the selection of the reference HMM (hidden Markov model) which best matches the noise type and SNR (signal to noise ratio) of the input testing speech, the estimation of the SNR value using the VAD (voice activity detection) algorithm and the classification of the noise type based on the GMM (Gaussian mixture model) have been done separately in the multi-model framework. As the SNR estimation process is vulnerable to errors, we propose an efficient method which can classify simultaneously the SNR values and noise types. The KL (Kullback-Leibler) distance between the single Gaussian distributions for the noise signal during the training and testing is utilized for the classification. The recognition experiments have been done on the Aurora 2 database showing the usefulness of the model compensation method in the multi-model based speech recognizer. We could also see that further performance improvement was achievable by combining the probability density function of the MCT (multi-condition training) with that of the reference HMM compensated by the D-JA (data-driven Jacobian adaptation) in the multi-model based speech recognizer.