In this study, a binaural microscopic model for the prediction of speech intelligibility based on the modulation filter bank is introduced. So far, the spectral criteria such as the STI and SII or other analytical methods have been used in the binaural models to determine the binaural intelligibility. In the proposed model, unlike all models of binaural intelligibility prediction, an automatic speech recognizer (ASR) is used in the back-end as the decision unit. One advantage of using this approach is the possibility of analyzing the recognition rate of small parts of speech such as phonemes and syllables. Another advantage of this model lies in the use of pre-processing that their existence in the human auditory system has been verified. Using the proposed feature matrix in the speech recognizer, this model has good predictions in the presence of one source of stationary speech-shaped noise. Comparing the results of the proposed model with those of listening tests show high correlations and low mean absolute error values. Also, the confusion matrices of the consonants represent high correlation between predictions and measurements. The predicted speech reception threshold by the proposed model has a smaller mean absolute error (0.6 dB) than the baseline model of BSIM.