Methods are available for computing properties of the waiting time associated with a variety of single-server queuing models in the equilibrium state. Since these calculations are more difficult in the time-dependent case, this paper develops an approximation procedure applicable to a wide class of single-server queues. Specifically, it considers the moments of the waiting time Wn of the nth arriving customer of the system GI/G/1 and (given certain conditions) uses an expansion related to the central limit theorem to derive approximations to these moments. The expectation EWn is treated in some detail, particularly for the Erlang system Ek/Em/1, and numerical illustrations are given. The same arguments apply to higher moments, but the calculations become tedious and details are not given.