<p>This paper mainly concentrates on the voltage and frequency restoration as well as the active power sharing in islanded AC microgrid (MG) under hybrid cyber attacks by applying the distributed secondary control scheme. Due to the reliance of the secondary control layer on communication networks that may bring potential network threats, a novel distributed cyber-resilient secondary controller is proposed to mitigate the impact of switching denial-of-service (DoS) attacks and impulsive deception attacks. The ability to resist cyber attacks of the MG is significantly enhanced by regulating the control gain parameters in the given simple-form inequality, which directly related to the secondary controller. Sufficient conditions for realization of the voltage and frequency restoration as well as the accurate active power sharing are presented, respectively, where the inconsistent matrix dimensions of the system under cyber attacks are dexterously handled by introducing a series of expanding diagonal matrices. Eventually, the effectiveness of the proposed theories is demonstrated in the simulation by a test islanded AC microgrid.</p>