In order to weaken the adverse effect of backlash nonlinearity on dual-motor driving servo system, an adaptive control strategy was proposed. The state-space model of the system was first given. By introducing the virtual control quantity, using backstepping approach and recursively selecting the Lyapunov function, and adopting a radial-basis-function (RBF) neural network to design adaptive law, a state feedback-based RBF neural network backstepping adaptive controller was designed, and its stability was analyzed. Compared with the conventional PID control in simulation results, the proposed control strategy shows better position tracking performance and higher robustness.