Based on probability distribution theory and L-K functional methods, the issue of probability-distribution-dependent load frequency stability is investigated for a class of power systems with time-varying delays. Firstly, by considering the probability distribution feature of the communication time-delay in the system modeling, the power systems with PI-based load frequency controller is converted to a closed-loop system with stochastic time-varying delay. Secondly, by fully using the probability distribution information of stochastic time-varying delays, a suitable L-K functional is constructed. Then, by employing the integral inequality and improved reciprocally convex combination technique to estimate the derivative of the L-K functional, some probability-distribution-dependent load frequency stability criteria are derived for the power systems. Finally, some case studies are applied to show the effectiveness and superiority of the design method.