Abstract: To address the effect of low inertia caused by the large-scale access of the renewable energy sources in the islanded microgrid systems and the communication delays in the open communication networks on the system stability, this paper investigates the load frequency control problem of the low-inertia islanded microgrid systems under the influence of time-varying delays. First, for the time-delayed microgrids, a hierarchical frequency control model with the additional virtual inertia control is proposed. Then, a new Lyapunov-Krasovskii functional is developed by introducing the delay-product-type term and the augmented s-dependent integral term. After that, to reduce the conservativeness of the main result, the constructed functional is effectively estimated by using the composite slack-matrix-based integral inequality, the quadratic inequality, and the convex combination. Finally, the simulations in different scenarios verify that the proposed method improves the time-delay stability margin and the dynamic performance of the islanded microgrids, and the relationships between the time-delay stability margins, and the controller parameters and the nonlinear load disturbances are also illustrated.