The open communication network has been widely used in modern load frequency control (LFC) for multi-area power systems, which poses a safety hazard to power systems. This paper investigates the problem of the design of resilient controller for load frequency control against periodic Denial-of-Service (DoS) attacks. Firstly, a detectable DoS attack modle is given. Then, a time delay switched distributed LFC system model is formulated under DoS attacks . Furthermore, the system stability of switched system is analyzed by using the Lyapunov theory, and a design method for resilient controller is proposed, which is robust to the load disturbance and cyber attack. Finally, the effectiveness of the proposed method is validated by a two-area power system in MATLAB/SIMULINK.