Most of the existing link prediction algorithms only study the first-order similarity between nodes and their neighbor nodes, without considering the high-order similarity between nodes and the neighbor nodes of their neighbor nodes. In order to solve this problem, a Link Prediction algorithm based on High-Order Proximity Approximation (LP-HOPA) was proposed. Firstly, the normalized adjacency matrix and similarity matrix of a network were solved. Secondly, the similarity matrix was decomposed by the method of matrix decomposition, and the representation vectors of the network nodes and their contexts were obtained. Thirdly, the original similarity matrix was high-order optimized by using Network Embedding Update (NEU) algorithm of high-order network representation learning, and the higher-order similarity matrix representation was calculated by using the normalized adjacency matrix. Finally, a large number of experiments were carried out on four real datasets. Experiments results show that, compared with the original link prediction algorithm, the accuracy of most of the link prediction algorithms optimized by LP-HOPA is improved by 4% to 50%. In addition, LP-HOPA can transform the link prediction algorithm based on local structure information of low-order network into the link prediction algorithm based on high-order characteristics of nodes, which confirms the validity and feasibility of the link prediction algorithm based on high order proximity approximation to a certain extent.