Conventional finite control set model predictive control (FCS-MPC) for multilevel converters can realize multi-objective control and contain the nonlinear characteristics. However, conventional FCS-MPC may lead to high computational complexity and unwanted switching transition, which is not easy to implement. To solve the issues of computational burden and unwanted switching transition, this paper proposes the fast FCS-MPC for three-phase five-level nested neutral point piloted (NNPP) converter. According to the switching principle, the finite control subset of the effective candidates is obtained from all of the switching combinations, which significantly reduces the necessary iterations and computational complexity. The proposed fast FCS-MPC also avoids output level jump and unwanted switching transition. Moreover, the neutral-point voltage balance and reducing switching frequency are also taken into account in the cost function. Finally, the five-level NNPP converter simulation model is built. The simulation results verify the correctness of the proposed fast FCS-MPC.