To improve the control performance for the dual-inertia system of a permanent magnet synchronous (PMSM) motor under the influence of uncertainty, this paper proposes a model-free recursive terminal sliding-mode control method based on a dual perturbation observer. First, a dual-inertia system model for the PMSM is established with uncertain disturbances. The model-free recursive terminal sliding mode controller that is devised by combining model-free control and recursive terminal sliding mode control enables the system state to be moved from the sliding mode surface at the beginning. This shortens the time for the state error to converge and effectively suppresses chattering. Then, a dual disturbance observer is designed by constructing an extended state observer to observe load speed and feed it back to an improved extended disturbance sliding mode observer. It accurately estimates the lumped disturbance signals and puts the feed-forward compensation to the controller, which further improves the steady-state performance and the anti-disturbance capability of the system. Finally, the superiority and effectiveness of the scheme is verified by simulation and experiment which contrasts it with proportional-integral and improved model-free sliding mode control.