A strategy for grid impedance estimation is proposed in this article. The strategy is based on the use of an observer suitable to implement the control and synchronization of a voltage-source inverter with an LCL filter, by measuring only the current that the system injects to the grid. The estimation is done based on the modification of the original structure of the observer, together with the implementation of a grid current injection strategy, which allows the observer to adapt in the presence of grid impedance uncertainty. The proposed strategy provides an accurate estimate of the grid impedance inductive and resistive components, suitable for control purposes. The validity and effectiveness of the proposed strategy are demonstrated by simulation and experimental results.