In mobile speech communication, speech signals can be severely corrupted by background noise when the far-end talker is in a noisy acoustic environment. To suppress background noise, speech enhancement systems are typically integrated into mobile phones, in which one or more microphones are deployed. In this study, we propose a novel deep learning based approach to real-time speech enhancement for dual-microphone mobile phones. The proposed approach employs a new densely-connected convolutional recurrent network to perform dual-channel complex spectral mapping. We utilize a structured pruning technique to compress the model without significantly degrading the enhancement performance, which yields a low-latency and memory-efficient enhancement system for real-time processing. Experimental results suggest that the proposed approach consistently outperforms an earlier approach to dual-channel speech enhancement for mobile phone communication, as well as a deep learning based beamformer.