This paper concerns the numerical approximation of the strong solution of the Itô stochastic delay differential equation (SDDE)
where , and is a Wiener process. A theorem is proved establishing conditions for convergence, in the mean-square sense, of approximate solutions obtained from explicit single-step methods. Then a SDDE version of the Euler-Maruyama method is presented and found to have order of convergence 1. The paper concludes with several figures illustrating numerical results obtained when this method is applied to an example.