The modular multilevel converter (MMC) becomes attractive in the medium- and high-power application with high modularity. In this paper, the MMC is proposed to be applied in the variable speed wind turbine (VSWT) based on the full-scale back-to-back (BTB) power converter, where the generator-side converter is the three-level neutral-point-clamped (NPC) converter and the grid-side converter is the three-phase MMC. A control strategy is also presented for the MMC based VSWT for the second-order harmonic current elimination. The proposed MMC based VSWT and control not only mitigate the voltage ripple in the dc-link of the power converter to improve system performance, but also ensure the grid-side current balancing to increase the generated power of the wind turbine under the unbalanced grid fault, in comparison with the conventional VSWT based on BTB three-level NPC converters. The simulation studies of the proposed MMC based VSWT and control are conducted with a detailed PSCAD/EMTDC model, and the results show their effectiveness.