Abstract: Aimed at the optimization problem of the fastest time climb of the passenger aircraft, the improved hp adaptive Radau pseudospectral method (RPM) is used to discretize the continuous-time optimal control of passenger aircraft climb into a nonlinear programming problem to solve. The experimental simulation results verify that the optimized aircraft climbing trajectory can complete the fastest time climbing under the premise of meeting the performance constraints of the passenger aircraft and the passenger experience, and achieve cruise altitude and cruising speed. Compared with the hp adaptive Radau pseudospectral method, the improved method can complete the optimization process with higher solving efficiency on the basis of ensuring the optimality of the optimization solution.