Model predictive control (MPC) suffers from high computational burden and cumbersome tuning of weighting factors especially for three-level three-phase inverters. Here a fast finite-switching-state model predictive control (FSS-MPC) algorithm without weighting factors is proposed. Firstly, the deadbeat (DB) solution is used to construct the voltage vector reference. Then, the T-type three-level three-phase inverter topology is selected and voltage vectors are carefully tuned in order to minimize the neutral-point (NP) voltage fluctuation. The voltage vectors that are far from the desired voltage vector reference and go against balancing the NP voltage are abandoned. Thus, only three effective voltage vectors instead of totally 27 vectors are required in the implementation of the proposed FSS-MPC algorithm, which saves computation time up to 46.7%. Furthermore, the proposed algorithm makes the tuning of the weighting factor unnecessary, which simplifies the practical implementation and improves the portability of the algorithm. Finally, an experimental prototype was established and main results including the steady-state and dynamic performance were presented to validate the effectiveness of the proposed algorithm.