Background and Objectives: To overcome the disadvantages of the traditional two-level inverters, especially in electric drive applications, multi-level inverters (MLIs) are the widely accepted solution. Diode-Clamped Inverters (DCIs) are a well-known structure of multi-level inverters. In DCIs, the voltage balance of the DC-link capacitors and the Common Mode (CM) voltage reduction are two important criteria that should be considered. Methods: This paper concentrates on the current control of 3-phase 4-level DCI with finite control set model predictive control (MPC) strategy. Current tracking performance, DC-link capacitor voltage balance, switching frequency minimization, and CM voltage control have been considered in the objective function of the MPC. Moreover, the multistep prediction method has been applied to improve the performance of the DCI. Results: The effectiveness of the proposed multistep prediction control for the 4-level DCI has been evaluated with different horizon lengths. Moreover, the effect of several values of weighting factors has been studied on the system behavior. Conclusion: Results validate the accuracy of current tracking and voltage balancing in the suggested multistep MPC for the 4-level DCI. In addition, CM voltage control and switching frequency reduction can be included in the predictive control. Decreasing the CM voltage and switching frequency will oppositely affect the dynamic behavior and voltage balancing of the DCI. Therefore, selection of weighting factors depends on the system needs and requirements.