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In order to solve the problem of insufficient power supply for helicopter and to increase the response speed of engine output power during the climbing process, the research on acceleration optimization control for the integrated helicopter/engine system is conducted. Meanwhile, the optimization control method with remarkable robustness for turboshaft engine based on torsional vibration suppression and min-batch gradient descent-neural network is proposed. The modified notch filter is available to suppress the torsional vibration from the frequency domain. Selecting the maximum output power as the optimization objective, the response speed of the engine output power can increase significantly through relaxing the restriction boundary of power turbine speed and taking into account the constraints of rotational speed, static strength, and temperature. The results show that the optimization control method can effectively reduce the low-order torsional amplitude by more than 70% and can decrease the response time of output power by more than 3s compared with the conventional cascade PID control, which allows the turboshaft engine to reach the potential on the premise of hardly exceeding the limit boundary.