Aiming at the trajectory optimization problem for single-stage-to-orbit aerospace vehicles involving combined-cycle propulsion during the ascent phase, this paper proposes an integrated adaptive convex optimization method for trajectory and parameters, which optimizes the ascent trajectory and mode transition points simultaneously. By considering a more comprehensive trajectory model and propulsion model with an integrated airframe-propulsion configuration, the vehicle’s attitude and propulsion control inputs are incorporated to accommodate its specialties and achieve better performance. A climb-dive maneuver is investigated to accommodate the difficulty of transient thrust decline and possibilities of start-up failure or stall of combined-cycle propulsion during the complicated mode transition phase. Numerical simulation results demonstrate that the proposed method achieves superiorities of the balance between solution accuracy and computational efficiency, and the Monte-Carlo execution proves its strong robustness.