This paper addresses the finite-time H∞ filtering for a class of nonlinear singular nonhomogeneous Markov jump systems by T-S fuzzy approximation approach, where the transition probabilities (TPs) are time-varying and unknown. First, by considering a stochastic Lyapunov functional and rendering the time-varying TPs inside a polytope, a sufficient condition on singular stochastic H∞ finite-time boundedness (SS H∞ FTB) for the filtering error systems is given. Then, by using the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition on the existence of the finite-time H∞ fuzzy filter is presented. The fuzzy filter is developed in terms of LMIs ensuring the filtering error system is SS H∞ FTB. Compared with the previous ones, the proposed design method in this paper has more freedom, leading to less conservative results. A tunnel diode circuit is provided to illustrate the effectiveness and advantage of the design approach proposed in this paper.