Abstract-As wind power technology points to increase power ratings, the implementation based on a permanent-magnet synchronous generator with a full power converter is expanding its market share. Multilevel converters, as for example, neutralpoint clamped converters, are therefore well suited for this application. Predictive current control presents similar dynamic response and reference tracking than other well-established control methods, but working at lower switching frequencies, and providing extensive flexibility to apply either on-line or off-line different control laws to the same plant. In this work, the predictive current control is applied to the both sides of the backto-back neutral-point clamped converter connecting a permanent-magnet synchronous wind power generator to the grid. Dc-link neutral-point balance is achieved by means of the predictive control algorithm, which considers the redundant switching states of the back-to-back neutral-point clamped converter. Reduced number of commutations, current spectrum control, and compliance with the low voltage ride-through requirement are carried out with the predictive control. The obtained experimental results confirm the suitability of the proposed control approach.