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In this paper, a sub-optimal trajectory optimization method is developed to generate trajectories for transition phases connecting two steady flights. Both control histories as well as the time step length that specify the trajectory for a transition maneuver are calculated as a root of an underdetermined system. Here, the unknowns are computed by a series of Newton iterations for finding the root, where explicit closed-form expressions are utilized within the algorithm to ensure computational efficiency. Moreover, a line-search strategy is incorporated to enhance the robustness. The terminal hard output constraints are guaranteed by the root finding, and the terminal control constraints are realized by using a time-varying weighting matrix in the cost function. Numerical simulations investigate multiple scenarios of transition phases, which show the effectiveness of the proposed method.