This paper addresses the quasi-synchronization issue of fractional-order multiplex networks with parameter mismatch using intermittent control. To provide a more comprehensive description of the complexity, ambiguity, and network topology in the real world, it simultaneously introduces parameter mismatch, intra-layer, and inter-layer structures into the mathematical model of fractional-order multiplex networks. Supported by graph theory and the Lyapunov method, and by employing an aperiodically intermittent control strategy, sufficient conditions are established for quasi-synchronization and estimate the allowable error bound. Finally, the theoretical results are applied to power systems and numerical simulations are presented to demonstrate the effectiveness of our findings.