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This paper introduces some robust stability conditions for a class of time delay systems whose uncertainties are assumed to be time-invariant and belong to convex bounded polytopic domain. Both single polyhedral and double polyhedral Lyapunov functionals are defined according to the form of Lyapunov-Krasovskii functional. And based on these functionals, the new results of robust stability analysis can reduce the conservatism of quadratic stability. All the proposed stability conditions are expressed in terms of linear matrix inequality (LMI). Two numerical examples are given to illustrate the advantages of the stability conditions based on the double polyhedral Lyapunov functional.