The objective of this dissertation is to investigate a fast and reliable method to generate three-dimensional optimal ascent trajectories for hypersonic air-breathing vehicles. The problem is notoriously difficult because of the strong nonlinear coupling amongst aerodynamics, propulsion, vehicle attitude and trajectory state. As such an algorithm matures, the ultimate goal is to realize optimal closed-loop ascent guidance for hypersonic air-breathing vehicles. The problem is formulated as a fuel-optimal control problem. The corresponding necessary conditions are given. It is shown how the original problem of search for the optimal control commands can be reduced to a univariate root-finding problem at each point along the trajectory. A finite difference scheme is used to numerically solve the associated two-point-boundary-value problem. Evaluation of the approach is done through open-loop solutions and closed-loop simulations. The results show promising potential of the proposed approach as a rapid trajectory optimization tool for the class of hypersonic air-breathing vehicles.