The application of Rontrvaqin's maximum principle to optimal control problems results in a two-point boundary value problem. The quasilinearization method is used to solve the resulting problem and the method is very effective if the final time is fixed. In this paper the modified quasilinearization with time transform is used to find the minimum time flight path in a vertical plane. The method is based on Newton-Raphson combined with long's method in order to solve the problem of unknown final time. The advantage of the method is the fact that it does not need large memary size compared with other methods of trajectory optimization. The minimum time trajectory of climb in a vertical plane is obtained after a few iterations which proves that the method is very efficient in this case.