In order to solve the trajectory optimization problem of air-breathing hypersonic missile， which can reflect its dynamic characteristics more truly and meet the requirements of multiple optimization indexes in the climbing phase， a trajectory optimization design method for air-breathing hypersonic missile with multi-degree-of-freedom is proposed. Under multiple constraints such as overload and dynamic pressure， the weighted summation method is used to design the double optimal target， and the hp adaptive pseudo-spectrum method is used to design and analyze the climbing trajectory of the air-breathing hypersonic missile. Simulation results show that this method can effectively solve the comprehensive optimization problem considering the minimum climb time and the minimum fuel consumption at the same time， and the multi-degree-of-freedom design can reflect the dynamic characteristics of the air-breathing hypersonic missile climbing stage more truly. Improved trajectory performance provides a new idea for trajectory optimization design of air-breathing hypersonic missile.