In recent years, voltage source multilevel converters are very popular in medium/high-voltage industrial applications, among which the NPC/H-Bridge converter is a popular solution to the medium/high-voltage drive systems. The conventional finite control set model predictive control (FCS-MPC) strategy is not practical for multilevel converters due to their substantial calculation requirements, especially under high number of voltage levels. To solve this problem, a hierarchical model predictive voltage control (HMPVC) strategy with referring to the implementation of g-h coordinate space vector modulation (SVM) is proposed. By the hierarchical structure of different cost functions, load currents can be controlled well and common mode voltage can be maintained at low values. The proposed strategy could be easily expanded to the systems with high number of voltage levels while the amount of required calculation is significantly reduced and the advantages of the conventional FCS-MPC strategy are reserved. In addition, a HMPVC-based field oriented control scheme is applied to a drive system with the NPC/H-Bridge converter. Both steady-state and transient performances are evaluated by simulations and experiments with a down-scaled NPC/H-Bridge converter prototype under various conditions, which validate the proposed HMPVC strategy.