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This study proposes a fault-tolerant control method for permanent magnet synchronous motors (PMSMs) based on the active flux linkage concept, which addresses permanent magnet (PM) demagnetisation faults in PMSMs. First, a mathematical model for a PMSM is established based on active flux linkage, and then the effect of PM demagnetisation on the PMSM is analysed. Second, the stator current in the static coordinate is set as the state variable, an observer is designed based on a sliding-mode variable structure, and an equation for active flux linkage is established for dynamic estimation based on the equivalent control principle of sliding-mode variable structure. Finally, the active flux linkage for the next moment is predicted according to the operating conditions of the motor and the observed values of the current active flux linkage. The deadbeat control strategy is applied to eliminate errors in the active flux linkage and realise the objective of fault-tolerant control. A timely and effective control for demagnetisation faults is achieved using the proposed method, which validity and feasibility are verified by the simulation and experiment results.