Abstract: A hydro-mechanical accelerator of one turbofan engine was chosen for the research.The decisive cam was designed by multi-optimal method using sequential quadratic programming(SQP) algorithm,wherein the object function was the evaluation function constructed by the rising time of the acceleration,overshoot and stabilization time with full consideration of the constraints in acceleration.The simulation results show that,the optimal design can reduce the overshoot of high pressure rotor speed,shorten the stabilization time and improve the acceleration performance.At the same time the maximum temperature before the turbine has sharply fallen,which is benefit to prolong the lifetime of turbine and other corresponding components.