The article deals with the Runge-Kutta method for the following neutral delay integro-differential equation
(, , are given functions). More precisely, the authors study the asymptotic stability of the Runge-Kutta method under small perturbations of the initial function . The main result of the article desribes conditions under that the Runge-Kutta methods are globally and asymptotically stable. This result improves the analogous theorem by Y. Yu, L. Wen and S. Li [Appl. Math. Comput. 191, No. 2, 543–549 (2007)]. In the end of the article, a numerical example is considered.