This paper considers an exponential zero-offset tracking problem for a class of nonlinear systems with model uncertainty and unmeasured disturbances. A nonlinear H-infinity-controller with exponential stability is firstly developed based on a technique in Lu and Doyle (IEEE Trans. Automatic Control 39 (1994) 2517) and then applied to establish a controller which guarantees exponential tracking with zero-offset of step reference signals. Further, a robust control scheme is designed to handle model uncertainties. Finally, the application of the new control method is demonstrated through simulations of controlling a pH neutralisation process in the presence of disturbances and model uncertainties.