This paper addresses a design of a fault detection observer (FDO) for descriptor linear parameter varying (D-LPV) systems. In contrast with the conventional approach for D-LPV systems, the gain scheduling functions (GSF) are considered unmeasurable. The FDO is investigated in the H-/H infinity index framework in order to minimise the effects of the disturbance and maximise the effect of faults on the residuals, and minimise the error caused by the unmeasurable GSF. The stability is guaranteed based on a Lyapunov approach. Sufficient conditions for the existence of the FDO are established in terms of linear matrix inequalities. The effectiveness of the proposed method is illustrated by means of a simulation example.