In networks, a link prediction task aims at learning potential relations between nodes to predict unknown potential linkage states. At present, most link prediction methods are used to process static networks. These methods cannot produce good prediction results for dynamic networks. However, for most dynamic networks in the real world, the vertices and links of these networks change over time. Dynamic link prediction (DLP) has attracted more attention as it can better mimic the evolution nature of the networks. Inspired by successful applications of the generative adversarial network in generating fake images, which are comparable with the real ones, we propose a novel generative dynamic link prediction (GDLP) method. Different from other DLP methods, we model the link prediction task as a network generation process. More specifically, GDLP utilizes the historical networks structure information to generate the network snapshot of next time stamp by an end-to-end deep generative model. This model contains a generator and a discriminator. The generator of GDLP is a spatiotemporal prediction model, which is responsible for generating the future networks based on the historical network snapshots, while the discriminator is a classification model to classify the generated networks and the ground-truth ones. With the two-player game training and learning strategy, GDLP is capable of accurate prediction for dynamic networks using the structural and temporal information. Experimental results validate that GDLP significantly outperforms several existing baseline methods on many types of dynamic networks, which improves the effectiveness of dynamic link prediction.