Energy internet has been highly promoted in most recent years, whose most obvious advantage is to provide bi-directional power flow and intellectual power sharing. Based on Benders decomposition (BD), a security constrained optimal power flow (SCOPF) model for corrective control in energy internet by using multi-microgrids is presented in this paper. Then an incentive control strategy that can effectively coordinate multi-microgrids and system generators to relieve post-contingency overflows is proposed. Comparing with the direct load control, the proposed control strategycan better encourage the bi-directional energy flow between the main grid and microgrids for post-contingency recovery. Numerical simulations on IEEE118-bus system demonstrate the effectiveness and efficiency of the proposed control strategy.