The problems of mixed $H_2/H_{infty}$ filtering design fer continuous and discrete time linear systems with time delay are investigated. The main purpose is to design a stable mixed $H_2/H_{infty}$ filter which minimizes the H$_2$Performance measure satisfying a prescribed H$_{infty}$ norm bound on the closed loop system in continuous-time case and discrete-time case, respectively. The sufficient conditions of existence of filter, the mixed $H_2/H_{infty}$ filter design method, and the upper bound of performance measure are proposed by LMI(linear matrix inequality) techniques in terms of all finding variables. Also, we present optimization problems in order to get the optimal mixed $H_2/H_{infty}$ filter in continuous and discrete time case, respectively.