In order to improve the dynamic response speed and reduce the total harmonic distortion of grid-connected current of the single-phase quasi-Z-Source Cascaded Multilevel Inverter (qZS-CMI), a total fraction deadbeat grid-connected control strategy is proposed. Firstly, for the difference of input power of each module of the cascaded quasi-Z source inverter, the module power scaling factor is defined and applied to the module power control to realize the module differentiated power distribution and maximum power output, and realize DC-link voltage balance of each module. Secondly, the grid-connected current and system feedback state quantity model is established, the deadbeat control strategy is used to realize the grid-connected current fast control. Finally, the effectiveness and correctness of the proposed algorithm are verified by the simulation model. This work is supported by National Natural Science Foundation of China (No. 51707126).