This paper deal with the problem of H∞ robust fault estimation for discrete time nonlinear system with a sector bounded nonlinear additive terms and multiple bounded state delay using the Takagi-Sugeno (T-S) fuzzy model. A fuzzy-fault estimation observer (FFEO) design is proposed to achieve fault estimation of T-S state delay models using fuzzy Lyapunov functions (FLF) with actuator and sensor faults. The disturbance rejection attenuation is constrained to a given level using a H∞-performance index. Sufficient conditions are established for the existence of the desired (FFEO) in terms of linear-matrix inequalities (LMIs). Finally, simulation results of numerical example is given to illustrate the effectiveness and applicability of the proposed method.