PMSG wind turbine system configured with three-level neutral-point-clamped (3L-NPC) back-to-back power converter and direct-drive train has good properties and is a nice solution for high power wind energy applications. Direct model predictive control has emerged as a viable alternative for power electronics and electrical drives. This work presents a direct model predictive current control (DMPCC) solution for both the grid and generator side control of grid-connected 3L-NPC back-to-back power converters in PMSG wind turbine systems. The presented DMPCC is realized all in alpha beta frame and evaluated all with experimental results on a fully FPGA based platform. Experimental results confirm both its effectiveness and its better steady state control performances in comparison with the conventional switching table based DTC-DPC technique.