Based on the Lyapunov-Krasovskii functional approach, the problem of robust stability of PID load frequency control is investigated for single-zone power system. Firstly, a system model for power system is established, which considers communication delays. Then, the system with PID controller is transformed into a closed-loop system with feedback control. By constructing an appropriate Lyapunov-Krasovskii functional and applying reciprocally convex inequality approach to deal with the integral terms in the functional derivatives, a new robust stability criterion is derived for power systems with PID parameters. Finally, a numerical example is given to illustrate the relationship between PI control gain and system delay stability margin under different time-delay types. The simulation results show the effectiveness and superiority of the method by comparing our results with existing ones.