This paper proposes an extended-state-observer-based distributed robust secondary voltage and frequency control for an autonomous microgrid (MG) with inverter-based distributed generators (DGs) considering the uncertainties from models and measurement noise. The MG is considered as a multi-agent system where each DG is defined as an agent and its controller only requires its own information and the information of its neighbors, but each DG obtains noisy measurements of the states of itself and its neighbors easily due to stochastic noise. Therefore, in this paper, an extended state observer is employed to estimate the accurate state information of each DG, which is significantly influenced by measurement noise. Furthermore, the distributed controllers based on a fast terminal sliding mode surface and an adaptive super-twisting algorithm are designed to track the voltage reference and to fasten the convergence rate against disturbances and uncertainties caused by parameter perturbation. Moreover, the distributed frequency controllers are also designed to restore the frequency and to guarantee the accurate active power sharing without power information of DGs. Finally, the effectiveness of the propose control strategy is illustrated by the simulation of an autonomous MG in MATLAB/Simulink.