In this paper an asymptotic numerical method is suggested to solve singularly perturbed weakly coupled system of convection-diffusion type second order ordinary differential equations with delay (negative shift) terms. An error estimate is derived in the supremum norm and it is found to be of order $O(N^{-1}\ln N)$ provided that $\varepsilon\leq C N^{-1}$, where $\varepsilon$ is small perturbation parameter and $N\ $ is the discretization parameter. Numerical results are provided to illustrate the theoretical results.