Finite-set predictive current control (FS-PCC) is advantageous for power converters due to its high dynamic performance and has received increasing interest in multilevel inverters. Among multilevel inverter topologies, the cascaded H-bridge (CHB) inverter is popular and mature in the industry. However, a main drawback of FS-PCC is its large computational burden, especially for the application of CHB inverters. In this paper, an FS-PCC method based on a deadbeat solution for three-phase zero-common-mode-voltage CHB inverters is proposed. In the proposed method, an inverse model of the load is utilized to calculate the reference voltage based on the reference current. In addition, a cost function is directly expressed in the terms of the voltage errors. An optimal control actuation is selected by minimizing the cost function. In the proposed method, only three instead of all of the control actuations are used for the calculations in one sampling period. This leads to a significant reduction in computations. The proposed method is tested on a three-phase 5-level CHB inverter. Simulation and experimental results show a very similar and comparable control performance from the proposed method compared with the traditional FS-PCC method which evaluates the cost function for all of the control actuations.