A multi-resolution version of the gammachirp envelope distortion index (mr-GEDI) is proposed for the intelligibility prediction of noisy speech processed using speech enhancement algorithms. The proposed model calculates the short-time signal-to-distortion ratio in the temporal envelope modulation extracted from the output of the gammachirp auditory filterbank. The predictions were compared with human subjective results for various signal-to-noise ratio conditions with pink and babble noise. The mr-GEDI predicts the intelligibility curves better than the hearing-aid speech perception index (HASPI).