Link prediction is an important issue in network analysis tasks, which aims at detecting missing, spurious or evolving links in a network, based on the topology information of the network and/or the attributes of the nodes. It has been applied to many real-world applications, such as information integration, social network analysis, recommendation systems, and bioinformatics. Existing link prediction methods focus on static networks and ignore the transmission of dynamic information in the network. However, many graphs in practical applications are dynamic and evolve constantly over time. How to capture time information in a dynamic network and improve the accuracy of link prediction remains a conspicuous challenge. To tackle these challenges, we propose a dynamic network representation based link prediction model, named DNRLP. DNRLP can be mainly divided into two modules: a representation learning module on dynamic network and a link prediction module, where the representation learning module is composed of a node information dynamic update unit and a node neighborhood update unit. Node information dynamic update unit leverages the benefits of the long short-term memory (LSTM) in capturing time information and uses a Time Interval based Filter Unit (TIFU) to introduce time interval information between two links, while for the node neighborhood update unit we present a random walk algorithm based on connection strength to simulate the diffusion of dynamic information. Through the above two parts, the model can obtain the node representation at the new moment, then link prediction is performed by the link prediction module by measuring the similarity between the node representations. The experiment uses MRR and Recall@k indicators to evaluate performance of model on four public dynamic network datasets. The experiments demonstrate the effectiveness and the credibility of the proposed model in link prediction tasks as compared with the comparison models, the MNR index of the DNRLP is increased by 30.8%. The model proposed in this paper not only learns the dynamic information in the network, but also considers its influence on neighbors and the impact of time interval on information update. Therefore, the model has learned more abundant dynamic information and has obvious advantages for link prediction tasks.