A direct, iterative method has been developed for the numerical solution of the transient few-group neutron diffusion and delayed precursor equations in three-dimensional, hex-z geometry. The method is shown to be numerically stable, and truncation errors are of order h2. The results of numerical experiments as well as comparison with space-time experimental results indicate that the method is accurate and that three-dimensional calculations can be performed at “reasonable” computing costs. The method is incorporated as a JOSHUA module at the Savannah River Laboratory.