In order to achieve high precision control of the dexterous hand, an adaptive neural network sliding mode control algorithm based on the U-K (Udwadia-Kalaba) equation is proposed. Firstly, based on the U-K equation and considering the ideal and non-ideal constrained force at each link of the dexterous hand, the detailed dynamic equation is derived. Secondly, considering the uncertainty of the non-ideal constrained force (mainly the friction force on each link of the dexterous hand) and the chattering phenomenon when using sliding mode control alone, the adaptive neural network and the sliding mode control algorithm are combined to realize the high-precision tracking and estimation of each link angle trajectory and the non-ideal constrained force. Finally, in order to verify the correctness and rationality of the proposed algorithm, the 3-DOF spatial dexterous hand is taken as the simulated object. The simulation results show that the tracking and estimation errors of each link angle and the non-ideal constrained force are 10(-2) order of magnitude.