In this paper, an algorithm applying adaptive wavelet neural network(AWNN) and sliding mode control(SMC) is proposed, investigated and exploited for tracking control of microelectromechanical(MEMS) gyroscope. Such an AWNN model can be regarded as a special radius basis function neural network, and utilizes Mexican hat function as activation function. Besides, Taylor expansion is used for analyzing activation radius which is considered as an adaptive variable. The parameters of MEMS gyroscope model are hard to obtain in engineering application, thus, AWNN and SMC are designed for approximating the uncertain function of MEMS gyroscope and the unknown asymmetrical dead zone in control scheme. The weights updating laws and the activation radius adaptive laws in AWNN are derived from the Lyapunov stability analysis, which result in the control error converging to the desired value and the weights and activation radius converging to its real value. Computer simulation results substantiate the theoretical analysis and further demonstrate the efficacy of such an algorithm combining with AWNN and SMC for MEMS gyroscope control.