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The vehicle dynamics and controls play a significant role in vehicle handling performance characteristics. The control of vehicle braking system and wheel slip is a challenging problem due to the nonlinear dynamics of the braking process and the wheel-road interaction. A simple and at the same time realistic vehicle longitudinal braking model is essential for such a challenging problem. In this paper, a new longitudinal rolling/braking quarter-vehicle model is presented. The proposed model takes both the rolling resistance force and the braking force into consideration and investigates their impact on the vehicle longitudinal dynamics. An anti-lock sliding-mode controller is designed to provide wheel slip control during vehicle motion. This type of controller is chosen due to its expected robustness against varying road friction coefficient.