[Objective] In the sensorless control system of permanent magnet synchronous motors, the traditional full-order sliding mode observer (FOSMO) adopts a fixed sliding mode gain, which fails to simultaneously balance the dynamic response speed and steady state performance of the system over a wide speed range. This leads to severe system chattering during the low speed operation of the motor, thereby reducing the observation accuracy of the rotor position and speed. [Methods] To address the aforementioned contradictions, this paper proposed an adaptive FOSMO based on current error and estimated speed. The sliding mode gain was dynamically adjusted according to the real-time operating state of the system, achieving smooth regulation under different operating conditions, thereby enhancing the dynamic performance and steady state accuracy of the system. Furthermore, to further suppress the chattering caused by high-frequency switching, a continuous and smooth hyperbolic tanh function was introduced to replace the traditional sign function. Meanwhile, the Lyapunov stability theory was employed to conduct mathematical derivation of the improved observer, which verified the convergence of the observer. [Results] The observation performance of the proposed adaptive FOSMO was verified through simulations and experiments. The results showed that, compared with the traditional FOSMO, the proposed adaptive FOSMO significantly suppressed the chattering of the extended back electromotive force waveforms and speed waveforms in the low speed region, remarkably reduced the rotor position estimation error, and achieved higher observation accuracy. [Conclusion] Under the proposed adaptive FOSMO, the system chattering is significantly suppressed, the overall stability of the system is improved, and the adaptive FOSMO has a wider applicable speed range.