This paper proposes an adaptive neural network composed of Gaussian radial functions for mapping the behavior of civil structures controlled with magnetorheological dampers. The online adaptation takes into account the limited force output of the semi-active dampers using a sliding mode controller, as their reaction forces are state dependent. The structural response and the actual forces from the dampers are used to adapt the Gaussian network by tuning the radial function widths, centers, and weights. In order to accelerate convergence of the Gaussian radial function network during extraordinary external excitations, the learning rates are also adaptive. The proposed controller is simulated using three types of earthquakes: near-field, mid-field, and far-field. Results show that the neural controller is effective for controlling a structure equipped with a magnetorheological damper, as it achieves a performance similar to the passiveon strategy while requiring as low as half the voltage input.