The core task of the stabilized platform in the rotary steerable system is to control the toolface angle, so that the trajectory of the whole bit can move forward to the set direction. Due to many downhole interference factors, the uncertainties of parameters related to internal friction and interference torque of stabilized platform always exist, which poses great challenges to model establishment and controller design. Moreover, the actuator dead-zone nonlinearity makes the control more complicated. Hence, a dynamic model of stabilized platform considering a variety of nonlinear factors is established, and an observer-based adaptive neural network (NN)-control law is proposed. An NN state observer is developed to cope with the uncertain states composed of unknown friction parametric uncertainties and unmodeled disturbances, the dead-zone inverse is constructed to compensate for a dead-zone, and the dynamic surface control (DSC) strategy is used to solve the “differential explosion,” all signals in the system are proved to be semi-global uniformly ultimately bounded (SGUUB) by the Lyapunov function. Finally, the MATLAB simulation is set up, and the accurate tracking effect of the system is proved by the simulation in the presence of friction, modeling error, and dead-zone nonlinearity. The validity and the superior performance of the proposed control method under the downhole harsh environment and parameter perturbation is verified by the comparison simulation experiments.