In this study, the problem of robust two-dimensional integrated guidance and control between an interceptor and a target is formulated and simulated by considering actuator faults in the interceptor. A robust model predictive control algorithm is employed to address this problem. To enhance system robustness against actuator faults, the fault is modeled in the state-space representation, resulting in an uncertain cost function. This cost function, in addition to tracking error and control signal variations, also accounts for uncertainties in the system's input matrix and is optimized over a finite horizon. By optimizing the cost function within a finite horizon, the complex differential equations are transformed into a set of algebraic equations. Consequently, the actuator fault compensation is incorporated into the optimization process, and the resulting control signal becomes a function of system uncertainties, thus achieving robustness against actuator faults. The proposed method solves a complex optimization problem while maintaining simplicity and practical implementability. Since the control signal is dependent on model uncertainties, the method improves closed-loop robustness under conditions of reduced actuator effectiveness due to faults, thereby mitigating the impact of actuator failures. To validate the performance of the proposed algorithm, various numerical simulations are carried out, and compared with several other methods.