This article presents a new algorithm of finite control set model predictive control (FCS-MPC) with floating virtual voltage vectors (VVs) applied to grid-connected voltage source converter. The new solution improves the conventional FCS-MPC and FCS-MPC with virtual VVs, assuring a fixed switching frequency. In comparison with FCS-MPC using virtual VVs, the proposed algorithm ensures a shorter distance between floating virtual VVs and actual voltage vector achieves lower THDi and ripples of the grid current for the same sampling time. The proposed control method has been experimentally validated using a 5-kW prototype. The algorithm was examined and compared in steady and transient states as well as under grid voltage disturbances, such as higher harmonics, dips, and unbalance. The simulation results and experimental measurements confirm that the developed control technique shows a high quality of the grid current (low THDi value), high dynamic performance, and immunity in case of weak grid conditions.