This paper considers set-membership estimation for discrete-time linear parameter-varying descriptor systems. Ellipsoid bundle, a new set representation tool combining certain characteristics of ellipsoids and zonotopes, is used to design a setmembership estimation method for the considered systems. We use the L∞ technique to design the estimator parameters in order to optimize estimation accuracy. This paper also studies the stability problem of the proposed method and establishes an offline sufficient stability condition. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.