This article studies the adaptive fuzzy asynchronous (AFA) stabilization of discrete networked hidden stochastic semi-Markovian switching power systems under cyber attacks. Due to the complex network environment, cyber-attacks are taken into account, in which the fuzzy logic rule is adopted to describe the unknown deception attacks. Considering the mismatch mechanism between the controller and the system, an adaptive fuzzy controller runs asynchronously with the system, where the hidden semi-Markovian model is used to characterize the asynchronous mechanism. Based on the detected mode and the fuzzy logic rule, an AFA stabilizing controller is designed for the underlying system. Using the stochastic Lyapunov function related to the detected mode and system mode, sufficient criteria are given for the AFA controller design, ensuring that the underlying system is bounded stable in the mean square. Finally, the proposed scheme is verified by the simulated example.