Average consensus problem in multi-agent systems has been an active topic allowing multiple agents to agree on the average of their initial values through local information interaction. However, the explicit sharing of state variables may lead to privacy disclosure problem. In this letter, a new approach is proposed to protect the initial state information of agents while ensuring convergence to the correct average consensus value. The core idea to achieve these goals is based on edge decomposition strategy. Agent divides its each connected edge into two edges, one edge is still connected to the original node, and the other edge is connected to a virtual node. Different from the existing state decomposition approach, our method changes from considering the nodes in network to considering the edges, which provides a new perspective for privacy protection. The correctness analysis and privacy analysis of the method are provided subsequently. Finally, numerical simulations are given to verify the effectiveness of our approach.