Energy-optimal adaptive cruise control (EACC) is becoming increasingly popular due to its ability to save energy. Considering the negative impacts of system noise on the EACC, an improved modified model predictive control (MPC) is proposed, which combines the Sage-Husaadaptive Kalman filter (SHAKF), the cubature Kalman filter (CKF), and the back-propagation neural network (BPNN). The proposed MPC improves safety and tracking performance while further reducing energy consumption. The final simulation results show that the proposed algorithm has a stronger energy-saving capability compared to previous studies and always maintains an appropriate relative distance and relative speed to the vehicle in front, verifying the effectiveness of the proposed algorithm.