In missions such as reconnaissance, unmanned aerial vehicles (UAVs) are required to rapidly fly through several waypoints and reach the target position. It is therefore necessary to ensure that the trajectory is constrained to pass through the intermediate points and the flight time is optimized. This paper proposes a multiple shooting parameterized differential dynamic programming (MSPDDP) algorithm. The validity of the MSPDDP algorithm is demonstrated through simulations of UAV multiple waypoint reconnaissance. Moreover, the trajectories optimized by MSPDDP are smoother and have a smaller inaccuracy than the MSDDP algorithm, which cannot optimize the time of flight.