Power system operator executes the unit commitment (UC) program to determine the optimal generation schedule for a daily or weekly horizon. In smart power systems, cyber-attacks such as false data injections (FDIs) may resemble a kind of contingency with only manipulating measurements data and without physical initiating events. This paper proposes a network constrained UC model in the presence of cyber-attacks named cyber-secured UC (CSUC) model. Normally the operating point obtained by UC program is on its conventional schedule, however in case of cyber-attack risk, it can depart from the conventional schedule toward the cyber secured schedule without violating unit and network constraints during such transition. The CSUC schedule is secured against a type of cyber-attacks called load redistribution (LR) attacks. Moving to this new operating point, in case of cyber-attack risk, may incur a small and reasonable additional cost to the cost of conventional generation schedule. In order to guarantee the optimality of solution, the proposed CSUC model is formulated as a mixed integer linear programming (MILP) model. The benders decomposition (BD) method is utilized to solve the model in a master and sub-problem hierarchy. The proposed method is implemented in the IEEE 118-bus test system.