This paper presents a new fuzzy speed controller based on a fuzzy angular acceleration observer to realize a robust speed control of permanent magnet synchronous motors(PMSM). The proposed speed controller needs the information of the angular acceleration, thus the first-order fuzzy acceleration observer is designed. The LMI existence condition is given for the proposed fuzzy speed controller, and the gain matrices of the controller are calculated. It is verified that the augmented control system consisting of the fuzzy speed controller and the fuzzy acceleration observer is mathematically stable. To validate the effectiveness of the proposed acceleration observer-based fuzzy speed controller, the simulation and experimental results are shown under motor parameter variations. It is definitely proven that the proposed control scheme can precisely track the speed of a permanent magnet synchronous motor.