In this paper, we deal with a system of non-linear integro - differential equations (IDEs) with constant time delay. Constructing a new Lyapunov Krasovskii functional (LKF) and using well-known result of Burton, [1, Theorem 4. 2.9]), we obtain and improve the result of Tian et al. [13, Theorem 1] to uniformly asymptotically stability of zero solution under weaker condition as well as we investigate the integrability of the norm of solutions and boundedness of solutions using that LKF. In particular cases, for illustrative aims, two numerical examples arc provided to show the uniformly asymptotically stability of zero solution as well as integrability and boundedness of solutions. By this work, we do a contribution the topic of the paper and relevant literature, and obtain and improve the result in Tian et al. [13, Theorem 1] under weaker conditions. The results of this paper have new contributions to the literature and they may be useful for researchers working on the mentioned concepts.