The existing methods ignore the adverse effect of knowledge graph incompleteness on knowledge graph embedding. In addition, the complexity and large-scale of knowledge information hinder knowledge graph embedding performance of the classic graph convolutional network. In this paper, we analyzed the structural characteristics of knowledge graph and the imbalance of knowledge information. Complex knowledge information requires that the model should have better learnability, rather than linearly weighted qualitative constraints, so the method of end-to-end relation-enhanced learnable graph self-attention network for knowledge graphs embedding is proposed. Firstly, we construct the relation-enhanced adjacency matrix to consider the incompleteness of the knowledge graph. Secondly, the graph self-attention network is employed to obtain the global encoding and relevance ranking of entity node information. Thirdly, we propose the concept of convolutional knowledge subgraph, it is constructed according to the entity relevance ranking. Finally, we improve the training effect of the convKB model by changing the construction of negative samples to obtain a better reliability score in the decoder. The experimental results based on the data sets FB15k-237 and WN18RR show that the proposed method facilitates more comprehensive representation of knowledge information than the existing methods, in terms of [email protected] and MRR.