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Summary: A Vienna rectifier is a kind of three‐phase converter with complex operation constraints. Traditional control methods suffer from poor dynamic responses and total harmonic distortion (THD), particularly when operating with adjustable wide‐range power. A novel low‐complexity model predictive control (LC‐MPC) algorithm is proposed based on the optimal switching vector sequence in this paper. First, a model predictive optimization control (MPOC) method is designed to search for the voltage vector sequence and its acting time. Second, the equivalent transformation and coordinate mapping of MPOC are efficiently achieved through the derived correlation factors and lookup table. Supported by the correlation factors, the redundant objective function calculation and repetitive online optimization are eliminated. Meanwhile, the simplified optimal over‐modulation strategy is implemented. Finally, the effectiveness and superiority of the algorithm are verified by comparative experiments. The results show that the proposed LC‐MPC is beneficial in terms of the computation time, dynamic response, over‐modulation, and harmonic content reduction. [ABSTRACT FROM AUTHOR]