The information about vehicle side-slip angle is essential given its relation to lateral stability and its importance for active safety control systems. Since direct measurement of the side-slip angle is expensive, developing efficient indirect techniques to extract this information from available sensor measurements is essential. This paper proposes a novel, cost-effective indirect strategy for the robust estimation of the side-slip angle using a state observer that relies on a discrete-time Linear Parameter Varying (LPV) lateral vehicle dynamic model. The proposed algorithm relies on a finite-time interval LMI-based observer, which accounts for the uncertainties on the model parameters (cornering stiffness) with known upper and lower uncertainty bounds. The simulation results show the effective and robust estimation performance of the proposed observer under various changes in system parameters. Moreover, comparison results with H∞ set-membership observer for discrete-time LPV systems show the effectiveness of the developed observer.