A procedure for the establishment of time optimal control policies for systems described by ordinary differential equations is presented. The method consists of introducing an augmented performance index and using iterative dynamic programming (IDP), in conjunction with a modified false position method to search for the minimum final time t(f). Numerical investigation of three examples indicate that results close to the time optimal control policy can be obtained without difficulty, even when the systems are highly nonlinear. This procedure is especially attractive if a personal computer is used for the computations.