The estimation of bus-voltage/branch-current and harmonics is an effective class of measures to monitor and improve the power quality of distribution grids. In this paper, we propose a robust iterative fuzzy observer method to estimate both voltage/current state variables and harmonic disturbances in distribution grids in the presence of uncertainties in the models used for design due to component aging or parameter drift. Overall, the observer is composed of a robust fuzzy nominal state observer and an iterative fuzzy harmonic observer, where the observer parameters are designed using a fuzzy method based on parallel distribution compensation. It should be noted that the online iterative termination condition of the fuzzy harmonic observer is determined based on the Total Harmonic Distortion of the output tracking error, in order to take into account both the online estimation speed and the estimation accuracy. Finally, a numerical simulation is given to verify the validity of these obtained conclusions.