The low-voltage ride through (LVRT) requirement demands the wind power plants to remain connected to the grid in the presence of grid voltage dips, actively helping the network overall control to keep network voltage and frequency stable. Wind power technology points to increase power ratings. Hence, multilevel converters, as for example, neutral-point-clamped (NPC) converters, are 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. In this paper, the predictive current control is applied to the grid-side NPC converter as part of a wind energy conversion system, in order to fulfill the LVRT requirements. DC-link neutral-point balance is also achieved by means of the predictive control algorithm, which considers the redundant switching states of the NPC converter. Simulation and experimental results confirm the validity of the proposed control approach.