Aiming at the excessive reliance on accurate models in permanent magnet synchronous motor (PMSM) control, a model-free adaptive fast terminal sliding mode control algorithm based on dynamic linearization is proposed. First, the motor motion equations are transformed into a discrete compact-form dynamic linearization model. Combining a novel fast power reaching law with the advantages of compact-form model-free adaptive control and discrete fast terminal sliding mode algorithm, a discrete-time model-free adaptive fast terminal sliding mode control law is designed. Second, based on the motor input and output data, a pseudo partial derivative (PPD) estimation algorithm is constructed according to a performance criterion, realizing fully data-driven control. The convergence of the PPD estimation and the stability of the control algorithm are analyzed. Finally, compared with conventional control strategies and model-free adaptive sliding mode control, simulation and experimental results show that the proposed method improves the response speed and robustness of PMSM drive systems, while eliminating the need for an accurate system model.