Dc-capacitor voltage drift phenomenon is the main technical issue of an n-level (n>3) Diode-Clamped Converter (DCC). This paper presents a predictive current control strategy for a three-phase five-level DCC which enables simultaneous control of ac-side currents and balance of capacitor voltages. The paper derives a discrete-time dynamic model of a five-level DCC. Based on the derived model, a predictive current control strategy is proposed. The proposed control strategy provides prominent features of ac-side current control and capacitor voltage balancing by using a simple and straightforward procedure. The performance of a five-level DCC with the proposed control method, under various operating conditions, is evaluated based on time-domain simulation studies in the MATLAB/SIMULINK environment. The simulation results demonstrate the capability of the proposed predictive current control to control the currents and to maintain voltage balance of the dc capacitors, simultaneously, without any requirement to complicated calculations.