The streaming ray technique was developed as a method for solving two-dimensional stationary transport problems. A formulation for applying a similar approach to the solution of one-dimensional time-dependent problems is given. As in the stationary case, use is made of an SN-type grid and a second independent grid comprised of streaming rays. For time-dependent problems, the streaming ray grid enables accurate tracking of wave fronts, while the SN grid provides a mechanism for the calculation of the scattering source. Sample calculations are given, and the results are in excellent agreement with analytical benchmark solutions.