In this paper, a novel decentralized control structure is proposed to compensate voltage and frequency deviations of an ac microgrid (MG) with higher bandwidth compared to the conventional control structure with no need for a communication network. This approach is realized by firstly employing finite control set model predictive control of voltage source converter at the primary control level. Then, an adaptive droop control is presented to keep the voltage and frequency of the MG stable in steady state and serve as a secondary level of hierarchical control. Therefore, the MG voltage and frequency are restored to the nominal value with a decentralized communication-free control structure. Simulation results verify the accurate frequency and voltage restoration as well as fast power-sharing during the transient and steady-state performance with no need for communication infrastructure.