This article addresses the output feedback control of micromechanical (MEMS) gyroscopes using neural networks (NNs) and disturbance observer (DOB). For the unmeasured system states, the state observer and the high gain observer are constructed. The adaptive NNs are investigated to approximate the nonlinear dynamics, including the known nominal terms and the system uncertainties caused by environmental fluctuations. For the time-varying disturbances, the DOB is utilized. The sliding mode control is employed to enhance the robustness. Through simulation verification, the output feedback control using NNs and DOB can adapt to the dynamics of MEMS gyroscope with unmeasured system speed, while an expected effective tracking performance is obtained in the presence of unknown system nonlinearities and external disturbances.