The efficient driving control of MEMS gyroscopes is an attractive way to improve the precision without hardware redesign. This paper investigates the sliding mode control (SMC) for the dynamics of MEMS gyroscopes using neural networks (NNs). Considering the existence of the dynamics uncertainty, the composite neural learning is constructed to obtain higher tracking precision using the serial-parallel estimation model (SPEM). Furthermore, the nonsingular terminal SMC (NTSMC) is proposed to achieve finite-time convergence. To obtain the prescribed performance, a time-varying barrier Lyapunov function (BLF) is introduced to the control scheme. Through simulation tests, it is observed that under the BLF-based NTSMC with composite learning design, the tracking precision of MEMS gyroscopes is highly improved.