Phase is important for perceptual quality of speech. However, it seems intractable to directly estimate phase spectra through supervised learning due to their lack of spectrotemporal structure in it. Complex spectral mapping aims to estimate the real and imaginary spectrograms of clean speech from those of noisy speech, which simultaneously enhances magnitude and phase responses of speech. Inspired by multi-task learning, we propose a gated convolutional recurrent network (GCRN) for complex spectral mapping, which amounts to a causal system for monaural speech enhancement. Our experimental results suggest that the proposed GCRN substantially outperforms an existing convolutional neural network (CNN) for complex spectral mapping in terms of both objective speech intelligibility and quality. Moreover, the proposed approach yields significantly higher STOI and PESQ than magnitude spectral mapping and complex ratio masking. We also find that complex spectral mapping with the proposed GCRN provides an effective phase estimate.