Finite control set-model predictive control (FCS-MPC) has been used in power converters due to its advantages, such as fast dynamics, multi-objective control, and easy implement. However, due to variable switching frequency, the harmonics of inverter output current spread in a wide range of frequency. Furthermore, a large amount of computation is required for the implementation of the traditional FCS-MPC method. Here, an improved FCS-MPC algorithm with fast computation and fixed switching frequency is proposed in this paper for two-level three-phase inverters. First, according to the principle of deadbeat control, the inverter voltage vector reference can be constructed. Then, the operation durations and sequences of different voltage vectors are determined according to the location of the inverter voltage vector reference and the cost functions of different voltage vectors. In this algorithm, the operation durations of different voltage vectors are arranged inversely proportional to their cost functions. Compared with the conventional fixed switching frequency FCS-MPC control, the number of sectors involved in the FCS-MPC calculation can be reduced from 6 to 1, which greatly improves the computation efficiency. Moreover, the delay due to digital implementation is effectively compensated in the proposed algorithm. Finally, experimental tests are carried out to verify the advantages of the proposed method in terms of both steady-state and dynamic performance.