Abstract: We studies the delay dependent stability problem of the system with two additive time-varying dela. It firstly establishes a second order convex optimization inequality, which is equivalent to the second order covex function. Secondly, a new constructed Lvapunov functional is constructed based on the additive time−varying delays property. Using the integral inequality and some other inequality technique to the derivative of the Lyapunov functionals, the delay-dependent stability condition is obtained which in terms of linear matrix inequalities. Finally, one numerical example is given to verify the effectiveness of the proposed method and the superiority of the results.