The fault detection problem of discrete time linear switched system is studied by using the robust fault detection filter in the framework of mixed H_{_}/H_∞. First of all, residual is obtained by constructing fault detection filter. For the purpose of improving the accuracy of fault detection, weighted H_∞ performance is used as the robustness indicator of residual to disturbance, and H_{_} performance is regarded as the sensitivity indicator of residual to fault. As a result, the problem of robust fault detection filter design is converted to a multi-objective solving problem under the mixed H_{_}/H_∞. performance index. Then, multiple Lyapunov functions and average dwell time approach are used for deriving the preliminary result of filter design. Moreover, the couple between Lyapunov matrix and system matrix is removed by introducing the slack variables, and less conservative results are obtained. All results are in the form of linear matrix inequality. Finally, a numerical example that the parameters of the fault detection filter are designed is given to show that the designed filter can realize the function of fault detection.