This paper is dedicated to the design of unknown input (UI) observers for linear parameter-varying (LPV) systems using algebraic matrix manipulation. First, a discussion is provided concerning the classical design approach, which requires the matching condition. This condition is satisfied for a class of systems having relative degree 1. Second, for the same class of systems, a new generalized approach is proposed for simultaneous state and UI estimation. It is demonstrated that the proposed approach is more general than the classical approach. Finally, an extension of the approach is provided for LPV systems with arbitrary relative degree. Simulation examples are provided to illustrate the main results of the paper.