In this paper, we provide a novel adaptive neural network backstepping control scheme for a special variable stiffness actuator (VSA) based on lever mechanisms with saturation inputs, output constraints and disturbances is presented here. In the controller designing, the prescribed performance-tangent barrier Lyapunov function (PP-TBLF) is introduced to ensure that both the prescribed performance bound of tracking error and the output constraints are not violated. In specific steps of backstepping control scheme, the Chebyshev neural network and the Nussbaum-type function are used to solve the unknown nonlinearities and unknown gain sign. Meanwhile, the inverse hyperbolic sine function tracking differentiator is exploited to solve the “explosion of complexity” caused by the differentiation of virtual inputs and also approximate the complex partial derivative caused by the auxiliary control signals. Finally, the stability of the whole scheme is proved by Lyapunov criterion and the simulation results are presented to illustrate the feasibility of the raised control strategy.