Slightly unbalanced grid voltage can cause large unbalanced current and non-characteristic harmonics in threephase uncontrolled rectifier. This study proposes an accurate model to analyse the performance of three-phase uncontrolled rectifier in slightly unbalanced grid. Three appreciative operation modes (three-phase rectifier, doublephase rectifier and single-phase rectifier with discontinuous rectifier current) in slightly unbalanced grid are discussed in detail in this study. Moreover, the closed-form analytical expressions for boundaries of modes are also derived. To further aid the designer, the curves of current unbalance, third harmonic current, output average voltage, output voltage droop and output voltage harmonic as function of loads under the condition of 2% voltage imbalance are illustrated. Then the design procedure of capacitor is given considering the influence of unbalance and harmonics in slightly unbalanced grid. Finally, a design case is expressed. The design results are realised in a 5 kW three-phase uncontrolled rectifier to verify the accuracy of the proposed models. The proposed model provides a tool for rapidly and accurately judging the impact of various loads on the rectifier performance in slightly unbalanced grid.