In this study, a novel speed control algorithm that combines the model-free adaptive discrete-time integral terminal sliding mode control (MFA-DITSMC) method and non-linear disturbance observer (NDO) is presented for a permanent magnet synchronous motor (PMSM) drive system. To improve the robustness and assure excellent response speed, the MFA-DITSMC method is proposed and the designed process of a speed controller is divided into two steps. Firstly, the motion equation of the PMSM is converted into a discrete-time form and then the compact-format dynamic linearisation model is obtained. Secondly, the MFA speed controller is constructed by using the DITSMC method. Moreover, aiming at the deterioration of control precision caused by unknown lumped disturbances that exist in a control system, the NDO is devised to estimate and further reject disturbance. Finally, the effectiveness of the proposed algorithm is illustrated by simulation and experiments, and the results demonstrate that the designed speed controller has satisfactory dynamic response performance and strong robustness.