Modeling and reasoning about the multi-turn dialogue history is a main challenge for building an intelligent chatbot. Memory Networks with recurrent or gated architectures have been demonstrated promising for conversation modeling. However, it still suffers from two drawbacks, one is relatively low computational efficiency for its complex architectures, the other is costly strong supervision information or fixed priori knowledge, which hinders its extension and application to new domains. This paper proposes an end-to-end memory network with multi-head attention. Firstly, the model adopts a method using word embedding combined with position encoding to represent text input; Secondly, it uses multi-head attention to capture important information in different subspaces of conversational interactions. Finally, multi-layered attention is stacked via shortcut connections to achieve repeatedly reasoning over the modeling result. Experiments on the bAbI-dialog datasets show that the network can effectively model and reason for multi-turn dialogue and has a better time performance.