In this paper we address the design of the controller for semi-active vehicle suspension system that employs an MR damper as the actuator. MR dampers are nonlinear devices which are difficult to model. Several MR damper forward models have been proposed; they can estimate the damping force of the device taking variables such as control voltage and velocity inputs. However, the inverse model, i.e., the model that computes the control variable is even more difficult to find due to the numerical complexity that implies the inverse of the nonlinear forward model. In our case, we develop a neural network able to reproduce such inverse dynamics. This neural network is connected to a backstepping controller that estimates the damping force to reduce the vibrations of the system. The performance of the controller is evaluated by means of simulations in MATLAB/Simulink.