The finite-control set model predictive control (FCS-MPC) algorithm faces challenges because of its high dependence on model accuracy and significant computational demands for three-level pulse width modulation (PWM) rectifier systems. To respond to these challenges, this paper proposes a data-driven neural network and sector judgment based FCS-MPC approach for three-level PWM rectifiers. First, building a data-driven neural network estimator to approximate uncertain parameters and control input gains in the mathematical model of the rectifier through a parallel learning approach. Second, the estimated system parameters are used in the finite set model prediction controller, the model-predicted formulas are reformulated to derive the predicted reference space voltage vectors, and only three candidate switching state voltage vectors are selected for computational optimization in each cycle according to different sector boundary conditions, which reduces the computational workload by \(89\%\) compared to 27 traversals of the traditional MPC for optimization in each cycle. Finally, using simulation comparison experiments, It has been verified that the introduced method can quickly track the predicted parameters and effectively decrease the total harmonic distortion (THD) besides reduce the active and reactive power fluctuations.