With the aim to solve the problem related to the power chattering and anti-disturbance performance of a photovoltaic (PV) inverter in master−slave-organized islanded microgrid, an anti-disturbance finite-time adaptive sliding mode backstepping (DFA-SMB) controller is designed in this paper. First, the topology and the second-order dynamic model of PV inverter are established based on constant DC voltage and constant reactive power control method. Subsequently, the backstepping method is adopted to perform the control of a high-order system. Moreover, a second-order sliding mode differentiator is used to realize the function of command-filter, solving the differential expansion problem caused by the derivation of virtual controller. Besides, the terminal sliding mode control (TSMC) is introduced into the q-axis controller and d-axis inner loop controller, increasing the robustness and reducing the convergence time of the system. Adaptive control and disturbance-observer (DO) are used to perform the adaptive estimation of model parameters and the observation of lumped disturbances, respectively, enhancing the dynamic characteristics of the controller. Finally, a master−slave-organized islanded microgrid with 100 kW PV array is established in MATLAB/Simulink. The results demonstrate that the proposed control method can effectively reduce power chattering and improve the anti-disturbance ability of the PV system.