Robust Model Predictive Control Theory (RMPC) which is firstly presented by Kothare et al. is reviewed. In order to use this theory for set-point control of first-order systems with uncertain time delay and gain, the state-space model of the system is extended in order to transform this structural uncertainty to parametric uncertainty. Furthermore, to remove steady-state error, an integral action is added to the controller. The performance of proposed method, i.e., RMPC with Integral Action (RMPC+I) is investigated by simulations and the experimental results are obtained considering several uncertainty circumstances. RMPC+I design technique - proposed in this paper - have good robustness and good steady-state properties in real time application.