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This paper presents a robust model predictive current controller with a disturbance observer (DO-MPC) for three-phase voltage source PWM rectifier. The new algorithm is operated with constant switching frequency (CF-MPC). In order to minimize instantaneous d- and q-axes current errors in every sampling period, CF-MPC is implemented by selecting appropriate voltage vector sequence and calculating duty cycles. The fundamental of this algorithm is discussed and the instantaneous variation rates of d- and q-axes currents are deduced when each converter voltage vector is applied in six different sectors. A Luenberger observer is constructed for parameter mismatch and model uncertainty which affect the performance of the MPC. The gains of the disturbance observer are determined by root-locus analysis. Moreover, the stability of the disturbance observer is analyzed when there are errors in the inductor filter parameter. The proposed method has an inherent rapid dynamic response as a result of the MPC controller, as well as robust control performance with respect to the disturbance due to use of the combined observation algorithm. Simulation and experimental results on a 1.1 kW VSR are conducted to validate the effectiveness of the proposed solution.