One of the most difficult challenges for modern manufacturing is reducing carbon emissions. This paper focuses on the green scheduling problem in a flexible job shop system, taking into account energy consumption and worker learning effects. With the objective of simultaneously minimizing the makespan and total carbon emissions, the green flexible job shop scheduling problem (GFJSP) is formulated as a mixed integer linear multiobjective optimization model. Then, the improved multiobjective sparrow search algorithm (IMOSSA) is developed to find the optimal solution. Finally, we conduct computational experiments, including a comparison between IMOSSA and the nondominated sorting genetic algorithm II (NSGA-II), Jaya and the mixed integer linear programming (MILP) solver of CPLEX. The results demonstrate that IMOSSA has high precision, good convergence and excellent performance in solving the GFJSP in low-carbon manufacturing systems.