Observer design for dynamical systems with both known and unknown time-varying parameters is of significant interest in a number of real-world applications. This class of systems has been rarely addressed in the existing literature. This paper develops an interval observer design methodology for linear parameter varying (LPV) systems with parametric uncertainty. With information on upper and lower bounds of the uncertain parameters, an interval observer that produces an envelope covering all possible state trajectories is presented. The application of the proposed algorithm in an important vehicle state estimation problem which aims at minimizing the worst-case envelope of the side-slip-angle estimate in the presence of uncertain tire cornering stiffness parameters and varying vehicle speed is presented. The obtained observer is evaluated in simulation using CarSim, a commercial industry-standard vehicle simulation software. The results verify the value of the developed observer design method. (C) 2015 Elsevier Ltd. All rights reserved.