This paper presents a finite control set Model Predictive Control (FS-MPC) approach for a grid-connected converter, particularly suitable for non-stiff grids where under low Short Circuit Ratio (SCR) the performance of the controller may get affected by variations in supply impedance value. In order to avoid this problem, a novel supply inductance estimator that is based on the grid currents variations between consecutive sampling instants fully integrated in the MPC algorithm, is proposed. The estimation is carried out in real-time and updates the predictive controller at every sampling instant, thus providing a quick adaptability to a change in supply inductance. Moreover, by knowing the estimated value of the supply impedance, the phase and amplitude difference between grid voltage and the voltage at the point of common coupling is compensated. The proposed approach has been verified through simulation and experiments on a 3-phase 2-level active front-end converter.