An adaptive prescribed performance sliding mode control (APPSMC) of Micro-Electro-Mechanical System gyroscopes is proposed for the trajectory tracking in the presence of parameter variations and external disturbances. Steady-state error, transient error and convergence rate are important performance indexes in gyroscope systems. However, these indexes have not been investigated and corresponding control methods are not investigated as well. The proposed APPSMC scheme can guarantee that the tracking error is strictly within a predefined performance bound and the convergence rate is no less than a predefined value. All the gyroscope parameters including the angular velocity can be correctly estimated by adaptive laws and the disturbance bound is estimated by a neural network estimator to alleviate the chattering problem. Simulation results demonstrate the effectiveness of the proposed adaptive prescribed performance sliding mode controller.