Abstract: The epidemic spread and control problem is studied, and a model with exact predicting precision is presented based on complex networks, in which the non-exponential spread and recover function is considered. The influence of removing edges and nodes from the network is considered in the control strategy, and the control parameters can be adjusted freely. Mathematical analysis for the model is presented through utilizing cavity theory. The analytical results are confirmed by simulation experiments. The experiments on control strategy show that it is very important for the control of epidemic for people with more social contacts.