In this paper, the 3 degrees of freedom (3-DOF) parallel robot (3-RRC) is taken as the research object. The Lagrange method is used to establish the reduced order dynamic equations of three branch chains. On the basis of the U-K (Udwadia-Kalaba) equation, the analytical expressions of ideal and non-ideal constrained forces are obtained. Then the complete dynamic model of 3-RRC parallel robot is established. In order to achieve high precision control of 3-RRC parallel robot, and fully considering the uncertainty of non-ideal constrained force and chattering problem in terminal sliding mode control algorithm, the neural network is used to adaptively adjust the gain of switching function and achieve universal approximation of the unknown non-ideal constrained force. The neural network terminal sliding mode control algorithm is proposed for the complete dynamic model of 3-RRC parallel robot, and the stability of the control system is proved by Lyapunov theorem. Finally, the simulation research is conducted on the 3-RRC parallel robot. Simulation results show that the tracking precision of angle positions and non-ideal constrained forces are all reached 10(-2) order, which realize the high precision control of the 3-RRC parallel robot, weaken the chattering phenomenon, and verify the correctness and effectiveness of the proposed dynamic model and control algorithm.