This paper considers the design problem of observer-based H output feedback control over the nonlinear Takagi-Sugeno (T-S) fuzzy systems with distributed delays．Firstly, delay-dependent sufficient conditions satisfy the H performance, are given for the stability analysis in terms of non-strict linear matrix inequality; then, the equivalent linear matrix inequality stability conditions can be obtained. Based on this, the solvable of the observer-based H output feedback control problem is proposed. Finally, a numerical example is given to illustrate the effectiveness of the design approach here.