Knowledge graph embedding is efficient method for reasoning over known facts and inferring missing links. Existing methods are mainly triplet-based or graph-based. Triplet-based approaches learn the embedding of missing entities by a single triple only. They ignore the fact that the knowledge graph is essentially a graph structure. Graph-based methods consider graph structure information but ignore the contextual information of nodes in the knowledge graph, making them unable to discern valuable entity (relation) information. In response to the above limitations, we propose a general graph transformer framework for knowledge graph embedding (TGformer). It is the first to use a graph transformer to build knowledge embeddings with triplet-level and graph-level structural features in the static and temporal knowledge graph. Specifically, a context-level subgraph is constructed for each predicted triplet, which models the relation between triplets with the same entity. Afterward, we design a knowledge graph transformer network (KGTN) to fully explore multi-structural features in knowledge graphs, including triplet-level and graph-level, boosting the model to understand entities (relations) in different contexts. Finally, semantic matching is adopted to select the entity with the highest score. Experimental results on several public knowledge graph datasets show that our method can achieve state-of-the-art performance in link prediction.