This paper presents a continuous control set model-predictive control with a receding horizon for a three-phase voltage-source inverter with an LCL filter. In this proposal, a reduced model of the converter with an embedded integrator and a Kalman filter are used to obtain the inverter-side currents without oscillation. Then, a cost function makes use of these currents to generate the optimum duty cycles for the space vector modulator. With the proposed method, active damping performances, a zero state error, and a reduction of the computational burden are achieved. Compared to the finite control set model-predictive control, the proposed method operates with a fixed switching frequency. Simulations and experimental results show that this proposal works correctly even in the case of grid harmonics and voltage sags.