Time-series forecasting in geo-spatial domains has important applications, including urban planning, traffic management and behavioral analysis. We observed recurring periodic patterns in some spatio-temporal data, which were not considered explicitly by previous non-linear works. To address this lack, we propose novel `Periodic-CRN' (PCRN) method, which adapts convolutional recurrent network (CRN) to accurately capture spatial and temporal correlations, learns and incorporates explicit periodic representations, and can be optimized with multi-step ahead prediction. We show that PCRN consistently outperforms the state-of-the-art methods for crowd density prediction across two taxi datasets from Beijing and Singapore.