This paper proposes a discrete-time fuzzy fractional-order sliding-mode control (Fuzzy-FOSMC) dual loop current controller for a three-phase LCL-type grid-connected converter (GCC) with reduced order. Conventional sliding-mode control (SMC) has been widely used in GCC due to its robustness to disturbances. However, the chattering in SMC may reduce the tracking performance of the controller, and even lead to system instability. To solve this problem, a Fuzzy-FOSMC controller is proposed in this paper. The introduced fractional-order term can suppress the chattering, and the fractional-order of FOSMC is further adjusted by the fuzzy controller to improve the overall system performance. In addition, the inner loop is implemented by a Fuzzy-FOSMC controller to ensure the tracking of the converter-side current, making the LCL-GCC converter behave like a controllable current source converter with a capacitive-inductive filter, the grid current control problem falls from a third-order to a reduced order system, which solves some difficulties on the design of most controller types. The stability of the two-stage PV system is analyzed. Finally, the effectiveness of the proposed controller is verified by experiments. •A FOSMC controller is proposed for converter-side current tracking control, which makes the converter to behave like a current source inverter with a CL filter. Compared with existing methods, it exhibits great advantages in current convergence speed, steady-state tracking error, robustness to filter parameter variations and dc-bus voltage changes.•To increase the system robustness, based on the fixed parameters of the FOSMC, a fuzzy controller is designed to adjust the fractional order of FOSMC, which could greatly suppress the chattering in conventional SMC.•By establishing the small signal model of the PV LCL grid connected inverter, the matrix of the overall linear state equation of the PV system including MPPT is obtained, and the stability analysis of the PV system is realized.