The problem of feedforward control for Tiltrotor Aircraft/Turboshaft Engine System is addressed by proposing a robust H∞ adaptive feedforward control method. Firstly, a comprehensive real-time mathematical model of the tiltrotor/engine system is established based on the principles of thermodynamics and aerodynamics. The demand torque prediction model for tiltrotor aircraft is established based on a neural network to obtain the unmeasured variable of load torque disturbance. To enhance prediction accuracy, an online correction method is proposed in this study to rectify the neural network model's predictive performance. Subsequently, a feedforward controller based on the LMI method of H∞ is proposed to address the design problem of the turboshaft engine's feedforward controller. Specifically, this paper further derives the condition for maintaining disturbance suppression at its original level when incorporating a feedback controller into the open-loop design of the H∞-based feedforward controller. The feedforward controller is enhanced with an adaptive robust compensation term to effectively counteract the impact of model uncertainty, thereby optimizing its immunity performance. In terms of the adaptive law, we improve the covariance adaptive law to address the incompatibility between traditional E-modified control law and covariance regulation, enabling their integration and ensuring stability. Finally, a simulation of the tiltrotor/engine system is conducted using the proposed methodology, which includes feedforward and adaptive control based on least square method. The verification results demonstrate exceptional anti-disturbance performance of the system.