This article studies reachable set estimation for linear discrete-time systems with time delay, which are influenced by unknown but bounded disturbances. We propose a novel reachable set estimation method based on zonotopes for the considered systems. The proposed method can estimate real-time reachable set under nonzero initial conditions. In order to increase estimation accuracy, we propose an iterative method to reduce the conservatism caused by the couplings between reachable sets at different instants. The effectiveness of the proposed method is illustrated by three numerical simulations.