Abstract: A simplified direct multiple shooting algorithm is presented in this paper. The algorithm is developed to solve a class of optimal trajectory problems with assigned initial state variables, assigned（or partly assigned） terminal state variables, free terminal time and bound constraint both on state and control variables. First, this class of problems is transformed to a Mayer problem with fixed terminal time. Then, a nonlinear programming problem is formed from the Mayer problem using direct multiple shooting technique in the light of Bock and Plitt' s work.Satisfactory numerical results are obtained when an implementation of the presented algorithm is used to solve two optimal flight trajectory problems. The first problem is to minimize the flight time of a hovercraft. The second one is a practical problem in space travel. It is to minimize the total stagnation point convective heating per unit area.Numerical calculations show that the algorithm presented in this paper has a good convergence and no strict demands for initial guess in dealing with a flight trajectory problem. So comculate a flight trajectory problem.