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We design a novel deep learning framework for multi-channel speech recognition in two aspects. First, for the front-end, an iterative mask estimation (IME) approach based on deep learning is presented to improve the beamforming approach based on the conventional complex Gaussian mixture model (CGMM). Second, for the back-end, deep convolutional neural networks (DCNNs), with augmentation of both noisy and beamformed training data, are adopted for acoustic modeling while the forward and backward long short-term memory recurrent neural networks (LSTM-RNNs) are used for language modeling. The proposed framework can be quite effective to multi-channel speech recognition with random combinations of fixed microphones. Testing on the CHiME-4 Challenge speech recognition task with a single set of acoustic and language models, our approach achieves the best performance of all three tracks (1-channel, 2-channel, and 6-channel) among submitted systems.