In order to improve the control performance of the grid-connected converter with LCL filter, a new finite control set model predictive control (FCSMPC) strategy was designed. AC/DC converters can bring many advantages when using LCL filters to connect to the grid, but there were also problems of grid current resonance and increased control complexity. The new scheme eliminated grid current low-order harmonics and reduces sensitivity to grid voltage distortion by incorporating active damping algorithms into the FCSMPC controller. The steady-state and transient tests of the new control strategy and the test under grid voltage disturbances were carried out using the grid-connected converter experimental platform. The experimental results showed that the new control scheme developed reduces the current harmonic content of the grid under the condition of grid voltage distortion, and has good dynamic performance and robustness.