This paper is concerned with observer-based fault detection filter design for a continuous-time networked control system (NCS) by taking packet dropouts and network-induced delays into account. An observer-based fault detection filter and a reference residual model are introduced to construct a novel model for the continuous-time NCS. To reduce the time for fault detection, a new data reconstruction scheme is proposed and the corresponding closed-loop model is established. Based on the established models, new fault detection filter design criteria are derived to asymptotically stabilize the residual system. The mutually exclusive distribution characteristic of interval time-varying delays is made full use to deal with integral inequalities for products of vectors. The designed fault detection filters can guarantee the sensitivity of the residual signal to faults. Simulation results illustrate the effectiveness of the proposed observer-based fault detection filter design.