Link prediction is one of the most important methods to uncover evolving mechanisms of dynamic complex networks. Determining these links raises well-known technical challenges in terms of weak correlation, uncertainty and non-stationary. In this paper, we presented a novel gated graph convolutional network (GCN) based on spatio-temporal semi-variogram (STEM-GCN). It learns spacial and temporal features in order to achieve link prediction in the dynamic networks. In this STEM-GCN model, we first utilized the spatio-temporal semi-variogram to obtain the spacial and temporal correlations from the dynamic networks. Its spacial correlation helped us determine the hyper-parameters of STEM-GCN and speed up its training. The correlation smoothing strategy is also introduced to eliminate the noise through temporal correlation and to improve the accuracy of link prediction. Finally, the network dynamics are captured by propagating the spacial and temporal features between consecutive time steps with stacked memory cell structures. The extensive experiments on real data sets demonstrated the effectiveness of the proposed approach for link prediction in dynamic complex networks.