In multi-channel speech enhancement and robust automatic speech recognition (ASR), beamforming can typically improve the signal-to-noise ratio (SNR) of the target speaker and produce reliable enhancement with little distortion to target speech. With this observation, we propose to leverage beamformed mixture, which has a higher SNR of the target speaker than the input mixture, as a weak supervision to train deep neural networks (DNNs) to enhance the input mixture. This way, we can train enhancement models using pairs of real-recorded mixture and its beamformed mixture, and potentially realize better generalization to real mixtures, compared with only training the models on simulated mixtures, which usually mismatch real mixtures. Evaluation results on the real-recorded CHiME-4 dataset show the effectiveness of the proposed algorithm.