This paper considers robust fault estimation in the finite frequency domain for linear continuous-time descriptor systems. Based on state augmentation, we propose a fault estimation observer with a non-singular structure. To attenuate the effect of unknown disturbance and fault variation on fault estimation, a fault estimation observer is designed in the finite frequency domain using H-infinity optimisation technique. With the design conditions formulated as a set of linear matrix inequalities, the presented fault estimation observer can be efficiently designed. The applicability of the proposed method is verified by numerical simulations of a multi-machine infinite bus system.