Tail-sitters combine the advantages of fixed-wing unmanned aerial vehicles (UAVs) and vertical take-off and landing UAVs, and have been widely designed and researched in recent years. With the change in modern UAV application scenarios, it is required that UAVs have fast maneuverable three-dimensional flight capabilities. Due to the highly nonlinear aerodynamics produced by the fuselage and wings of the tail-sitter, how to quickly generate a smooth and executable trajectory is a problem that needs to be solved urgently. We constrain the speed of the tail-sitter, eliminate the differential dynamics constraints in the trajectory generation process of the tail-sitter through differential flatness, and allocate the time variable of the trajectory through the state-of-the-art trajectory generation method named MINCO. Because we discretize the trajectory in time, we convert the speed constraint on the vehicle into a soft constraint, thereby achieving the time-optimal trajectory for the tail-sitter to fly through any given waypoints.