Recent advances in Knowledge Graph Embedding (KGE) allow for representing entities and relations in continuous vector spaces. Some traditional KGE models leveraging additional type information can improve the representation of entities which however totally rely on the explicit types or neglect the diverse type representations specific to various relations. Besides, none of the existing methods is capable of inferring all the relation patterns of symmetry, inversion and composition as well as the complex properties of 1-N, N-1 and N-N relations, simultaneously. To explore the type information for any KG, we develop a novel KGE framework with Automated Entity TypE Representation (AutoETER), which learns the latent type embedding of each entity by regarding each relation as a translation operation between the types of two entities with a relation-aware projection mechanism. Particularly, our designed automated type representation learning mechanism is a pluggable module which can be easily incorporated with any KGE model. Besides, our approach could model and infer all the relation patterns and complex relations. Experiments on four datasets demonstrate the superior performance of our model compared to state-of-the-art baselines on link prediction tasks, and the visualization of type clustering provides clearly the explanation of type embeddings and verifies the effectiveness of our model.