This paper addresses the mixed ℋ−/ℋ∞ fault detection observer design issue for a class of linear parameter-varying (LPV) systems. Analogous to the definition of the quadratic ℋ∞ performance for LPV systems and the ℋ− index for linear time invariant (LTI) systems, the quadratic ℋ− index and the affine quadratic ℋ− index for LPV systems are defined in terms of linear matrix inequalities (LMIs). The first algorithm for designing the mixed ℋ−/H∞ observer is proposed, which aims at minimizing the quadratic ℋ∞ performance and maximizing the quadratic ℋ− index of the observer error dynamic systems. To reduce the conservativeness of this algorithm, the affine quadratic ℋ∞ performance and the affine ℋ− index for LPV systems are utilized. The robustness conditions and affine ℋ− index conditions for the underlying observer optimization issue are formulated as parameter-dependent LMIs. The Gridding technique and multi-convexity concept are applied, respectively, for reducing the parameter-dependent LMIs to finite LMI constraints. Correspondingly, two iterative algorithms are proposed. Furthermore, the threshold design and the estimation of the worst undetectable fault size are investigated. An example is studied to demonstrate the effectiveness of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd.