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 grid. 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 model is given. Then, a time delay switched distributed LFC system model is formulated under DoS attacks. Furthermore, the stability of switched system is analyzed based on the Lyapunov theory. 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 establishing a two-area power system model in Matlab/Simulink.