Summary: This paper considers the problem of time delay-dependent exponential stability criteria for the time-delay linear system. Utilizing the Linear Matrix Inequalities (LMIs) and slack matrices, a novel criterion based on the Lyapunov-Krasovskii methodology is derived for the exponential stability of the time-delay system. Based on the criteria condition we conclude that the upper bound of the exponential decay rate for the time-delay system can be easily calculated. In addition, an improved sufficient condition for the robust exponential stability of uncertain time-delay system is also proposed. Numerical examples are provided to show the effectiveness of our results. Comparisons between the results derived by our criteria and the one given in P. L. Liu [”Exponential stability for linear time-delay systems with delay dependence”, Journal of the Franklin Institute, 340, 481–488 (2004; Zbl 1035.93060)], S.Mondie and V.L.Kharitonov [”Exponential estimates for retarded time-delay system a LMI approach”, IEEE Transactions on Automatic Control, 50, 268–273 (2005)], and S.Xu, J.Lam and M.Zhou [”New exponential estimates for time-delay systems”, IEEE Transactions on Automatic Control, 51, 1501–1505 (2006)] show that our methods are less conservative in general. Furthermore, numerical results also show that our criteria can guarantee larger exponential decay rates than the ones derived by [Liu, loc. cit.] and [Mondie, loc. cit.] in all time delay points we have tested and in some of time delay points obtained by [Xu, loc. cit.].