© 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group. An improved iterative observer for fault estimation of discrete-time T-S fuzzy systems is discussed in this paper. A discrete mean value convergence lemma is proposed firstly. Based on this lemma, a sequence of iterative observers are constructed to estimate the unknown fault. By choosing a general Lyapunov function, conditions for the resultant augmented system to be asymptotically stable with the required (Formula presented.) performance are built in the framework of linear matrix inequalities. With the established conditions, an iterative algorithm is developed to realise the fault estimation. A numerical example is provided to verify the effectiveness of the proposed method.