This paper designs a perturbation observer based robust fractional-order PID control (PORF-PID) scheme to achieve the maximum power point tracking (MPPT) of photovoltaic (PV) inverters. At first, the PV inverter nonlinearities, parameter uncertainties and unmodelled dynamics are aggregated into a perturbation, which is then estimated online by a sliding-mode perturbation observer (SMPO). In addition, the perturbation estimate is fully compensated in the real-time by a robust fractional-order PID control (FPID), such that a global control consistency could be realized in the presence of various operation conditions. Due to the use of fractional-order control framework, the additional controller parameters could further improve the dynamical responses of the closed-loop system. Two case studies are carried out, e.g., solar irradiation variation and power grid voltage drop, to verify the effectiveness of the proposed approach. Simulation results demonstrate that PORF-PID control can achieve the fastest dynamical responses and the lowest overshoot in comparison to that of conventional PID control, FPID control, and feedback linearization control (FLC) under different operation conditions.