Secondary frequency control is one of the most effective measures to ensure the stable operation of islanded microgrids (MGs). Most research on secondary frequency regulation has only focused on realizing steady-state operation objectives, that is, frequency restoration and power sharing. However, improving the dynamic performance of secondary frequency control is of great importance, especially in synchronous distributed energy resources. These synchronous units can introduce undesired oscillation modes, which may cause the instability conditions of MGs. To improve the dynamic performance of islanded MGs, a membership-function (MF) -based control strategy is proposed. The proposed strategy can trade-off between transient frequency regulation and frequency error elimination using the MF values calculated by the time-stamped synchronized measurements of distribution-level phasor measurement units. Besides, considering the time-varying communication delays in secondary frequency control loops, an adaptive delay compensator is proposed. The weights of the proposed compensator are updated by real-time delay measurements to compensate for the phase lag of control signals. Therefore, the adverse effect of communication delays on secondary frequency control is weakened effectively. Numerical simulations on an IEEE 34-bus system and a typical 40-bus islanded MG system demonstrate the advantages of the proposed method in the secondary frequency regulation of islanded MGs.