In order to further utilize near-field speech data to improve the performance of far-field speech recognition, this paper proposes an approach to integrate knowledge distillation with the generative adversarial network. In this work, a multi-task learning structure is firstly proposed to jointly train the acoustic model with feature mapping. To enhance the acoustic modeling, the acoustic model trained with far-field data (student model) is guided by an acoustic model trained with near-field data (teacher model). Such training process makes the student model mimics the behavior of the teacher model by minimizing the Kullback-Leibler Divergence. To improve the speech enhancement, an additional discriminator network is introduced to distinguish the enhanced features from the real clean ones. The distribution of the enhanced features is further pushed towards that of the clean features through this adversarial multi-task training. Evaluated on AMI single distant microphone data, the method achieves 5.6% relative non-overlapped word error rate (WER) and 4.7% relative overlapped WER decrease over the baseline model. Evaluated on AMI multi-channel distant microphone data, the method achieves 6.2% relative non-overlapped WER and 4.1% relative overlapped WER decrease over the baseline model. Evaluated on the TIMIT data, the method can reach 7.2% WER reduction. To better demonstrate the effects of generative adversarial network on speech enhancement, the enhanced features is visualized and the effectiveness of this method is verified.