Abstract: This paper deals with the problem of designing a guaranteed cost modified repetitive control system based on two dimensional (2D) hybrid model for a class of linear systems with parametric uncertainties. First, by analyzing of the continuous control process and discrete learning process independently, the structure of a feedback modified repetitive control (FMRC) system is given and a hybrid continuous-discrete 2D model for the FMRC system is established. Then, the FMRC design problem is converted to the design problem of the continuous-discrete 2D systems with a state feedback. Next, by using the 2D Lyapunov theory, a sufficient condition for existence of guaranteed cost modified repetitive control is obtained. Furthermore, it is pointed out that the condition is equivalent to the solvability problem of a linear matrix inequality. Finally, the design problem of the optimal guaranteed cost control is formulated in solution of the associated convex optimization problem. The validity of the method is verified by a numerical example.