Microgrippers driven by piezoelectric actuators have been widely applied in various fields demanding high accuracy. However, it is challenging to achieve a higher precision due to the presence of hysteresis and disturbances. This brief presents a new approach to achieve a precision motion control by overcoming the mentioned problems. The reported solution is derived by integrating three main components, i.e., the online estimation of unknown parameters for the ideal plant, the position prediction with Kalman filter, and an adaptive sliding mode control algorithm. The estimated parameters converge to their real values, which are guaranteed by Lyapunov criterion. Using the estimated parameters, the position is predicted with the Kalman filter. The adaptive law and the control law are designed based on sliding mode strategy to attenuate the influence of the unknown and unmodeled parts. The stability of the control system is proved by resorting to Lyapunov theorem. The effectiveness of the proposed control approach is verified through simulation and experimental investigations on a prototype gripper device.