In this paper, the problem of designing a tracking controller for uncertain nonlinear state-delay systems that can suppress the effects of both unknown uncertainties and disturbances is investigated. The controller is designed by using the sliding-mode control concept and the polynomial approximation method. One of the features in this paper is that model uncertainties and state-delay terms are expressed as the Legendre polynomials expansion. The expansion coefficients of the Legendre polynomials can furthermore be modified by the update law derived from the Lyapunov stability theorem. The presented composite nonlinear controller, which consists of a sliding-mode controller with a coefficient update law and a sliding-mode observer, can achieve offset-free performance. The major advantage of the proposed control system design is to track the set point without producing a vigorous control action and requiring the exact knowledge of model uncertainties. The control scheme is illustrated by an example of a chemical reactor with delayed states. Simulation results indicate that the proposed method can work for processes with time delays, despite unknown modeling uncertainties.