An improved quasi-static method is applied to the time-dependent, three-dimensional neutron transport equation with explicit representation of delayed neutrons. The relevant equations are derived, and the corresponding implementation of the method is presented. The resulting new code, which uses a three-dimensional, discrete ordinates code (TORT) to solve the static fixed-source equations, is tested using transient benchmark problems that are available in the literature. Results obtained with the new time-dependent code, named TDTORT, are in satisfactory agreement with the benchmark problem results.