This paper is concerned with the output-feedback stabilization problem for a class of singular linear parameter-varying (LPV) systems. The objective is to design a dynamic output-feedback controller such that the resulting closed-loop system is robustly admissible. Different from the classical gain scheduling techniques, it is assumed in this paper that the scheduling parameters involved in the plant model are not exactly available for the controller. First, a sufficient and necessary condition for the solvability of the underlying stabilization problem is obtained in the form of general parameter dependent matrix inequalities. Second, an equivalent transformation is developed to convert the general parameter-dependent conditions into parameter-dependent linear matrix inequalities (LMIs). Third, the singular LPV system whose coefficient matrices take a polytopic form is considered, and the finite LMI-based conditions are derived. Finally, an illustrative example is provided to show the effectiveness of the proposed design methods. (C) 2019 Elsevier Ltd. All rights reserved.