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A linear parameter-varying model predictive control (LPVMPC) is proposed to enhance the longitudinal vehicle speed control of a gas-engine vehicle, with potential application in autonomous vehicles. To achieve this objective, an advanced vehicle dynamic model and a sophisticated fuel consumption model are derived, forming a control-oriented model for the proposed control system. The vehicle dynamic model accurately captures the motions of the tires and the vehicle body. The fuel consumption model incorporates new powertrain modes such as automatic engine stop/start, active fuel management, and deceleration fuel cut-off, etc. The performance of the proposed LPV-MPC is evaluated by comparing it to a PID controller. Both simulation tests and vehicle-in-the-loop tests demonstrate the superior performance of the proposed controller. The results indicate that the LPV-MPC provides improved longitudinal vehicle speed control and reduced fuel consumption.