In this article, the fault detection (FD) problem for a class of discrete-time Markov jump linear system (MJLS) with partially known transition probabilities is investigated. The proposed systems are more general, which relax the traditional assumption in Markov jump systems that all the transition probabilities must be completely known. A residual generator is constructed and the corresponding FD is formulated as an H filtering problem by which the error between residual and fault are minimised in the H sense. The linear matrix inequality-based sufficient conditions for the existence of FD filter are derived. A numerical example on a multiplier-accelerator model economic system is given to illustrate the potential of the developed theoretical results.