This paper presents an effective model predictive current control scheme for induction machines driven by a three-level neutral point clamped inverter, called variable switching point predictive current control. Despite the fact that direct, enumeration-based model predictive control (MPC) strategies are very popular in the field of power electronics due to their numerous advantages such as design simplicity and straightforward implementation procedure, they carry two major drawbacks. These are the increased computational effort and the high ripples on the controlled variables, resulting in a limited applicability of such methods. The high ripples occur because in direct MPC algorithms the actuating variable can only be changed at the beginning of a sampling interval. A possible remedy for this would be to change the applied control input within the sampling interval, and thus to apply it for a shorter time than one sample. However, since such a solution would lead to an additional overhead which is crucial especially for multilevel inverters, a heuristic preselection of the optimal control action is adopted to keep the computational complexity at bay. Experimental results are provided to verify the potential advantages of the proposed strategy.