Abstract: The robust guaranteed cost filter design problem for linear uncertain system is studied, including continuous-time and discrete-time systems. The design idea of the guaranteed cost filter is adopted. The convenient test approach for the existence of robust guaranteed cost filter is presented in the form of linear matrix inequality (LMI). Moreover, the parameters of the filter are determined directly by solutions of the LMI. If the robust guaranteed cost filter exists, the cost matrix can be optimized to get the optimal robust guaranteed cost filter. At last, a simulation example is given and the results demonstrate the effectiveness of the approach.