In recent years, due to fast dynamic response, no modulator and multi-constraint control, the finite control set model predictive control (FCS-MPC) has been widely employed in power converters. However, the computational burden of traditional FCS-MPC is relatively heavy owing to traversing all possible voltage vectors. In this paper, a novel FCS-MPC algorithm is proposed for LCL-type grid-connected inverters. Firstly, the weighted average inductor current (WAIC) algorithm is utilized to lower the order of the LCL filter model. Then, based on the idea of deadbeat control, the expected inverter output voltage vector is calculated according to the grid-injected current reference. Depending on the desired voltage vector, the optimal voltage vector which minimizes the constructed cost function is selected from its neighboring voltage vectors. Compared with the traditional FCS-MPC techniques, the proposed control algorithm can decrease the candidate voltage vectors from eight to three, which effectively reduces the computational complexity of the algorithm. A simulation model and experimental platform of a two-level three-phase grid-connected inverter are established to prove the performance of the proposed algorithm.