A new hybrid method was developed for the solution of the one-dimensional time-dependent diffusion equation in four energy and four delayed-neutron groups. Using this method it is possible to reduce the cost per problem solved by an order of magnitude compared with commonly used digital methods. The solution is based on discretizing the multigroup diffusion equation with respect to the spatial variable while leaving the time variable continuous. The simple coupled time-dependent differential equations so obtained are integrated continuously and in parallel for each of the reactor regions. The regional boundary values are updated from iteration to iteration until convergence is obtained. Two examples are presented in which the hybrid and digital solutions are compared for a fast plutonium oxide fueled reactor. The agreement between the hybrid and digital solution is fairly good.