Knowledge graph embedding aims to embed entities and relations into a low-dimensional continuous vector space. Due to the data sparsity of knowledge graphs, the performance of knowledge graph embedding is poor in vector representation. Since the type information of entities encompasses rich semantic information, it is introduced to improve the performance. However, the existing methods either do not support the hierarchical structure of type information or the type constraint of relations or complicate the model of the hierarchical structure. This study proposes a novel knowledge graph embedding method combining with hierarchical type information. Specifically, types are embedded into different vector spaces and the hierarchical structure of types is modeled by the partial order relation. Moreover, the vector representations of entities are mapped into the type vector space so that entities and their types can be required to satisfy the partial order relation. The entities and their type constraint of relations in triples are also made to satisfy the partial order relation. Finally, experimental results of link prediction, triple classification and entity typing task on four datasets show that the proposed method outperforms the state-of-the-art baseline methods in vector representation performance.