The increased demand for robotic manipulator has driven the development of industrial manufacturing. In particular, the trajectory tracking and contact constant force control of the robotic manipulator for the working environment under contact condition has become popular because of its high precision and quality operation. However, the two factors are opposite, that is to say, to maintain constant force control, it is necessary to make limited adjustment to the trajectory. It is difficult for the traditional PID controller because of the complexity parameters and nonlinear characteristics. In order to overcome this issue, a PID controller based on fuzzy neural network algorithm is developed in this paper for tracking the trajectory and contact constant force simultaneously. Firstly, the kinetic and potential energy is calculated, and the Lagrange function is constructed for a two-link robotic manipulator. Furthermore, a precise dynamic model is built for analyzing. Secondly, fuzzy neural network algorithm is proposed, and two kinds of turning parameters are derived for trajectory tracking and contact constant force control. Finally, numerical simulation results are reported to demonstrate the effectiveness of the proposed method.