The simplification and steady-state performance issues of the model predictive control (MPC) are arising especially for multilevel converter topologies. For addressing these problems, this paper puts forward a simplified model predictive current control (MPCC) for single-phase cascaded H-bridge rectifiers, which can meet the challenge of good steady-state performance and capacitor voltage balancing. The constant switching frequency is achieved by applying predefined switching sequence. The duration of the redundant vectors is tuned by proportional-integral (PI) controller to realize capacitor voltage balancing, leading to the ease of redundant voltage vectors lookup table. Without evaluating cost function with all the voltage vectors by enumeration, redundant voltage vectors simplification and optimal switching sequence solving are utilized, which can remarkably simplify the complexity of the MPCC method. Finally, a hardware-in-loop experimental platform with DSP TMS320F28335 + RT-LAB real-time simulator is developed to compare and test the traditional and proposed MPCC scheme. Experimental results are conducted to verify the validity of the proposed MPCC method.