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This paper is concerned with the problem of delay-dependent robust H∞ control for uncertain time-delay fuzzy systems with norm-bounded uncertainty. The time-delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds for the delay are available. No restriction on the derivative of the time-varying delay is needed, which allows the time-delay to be a fast time-varying function. The state-space Takagi-Sugeno (T-S) uncertain fuzzy model with interval time-varying delay is adopted. Delay-dependent conditions for the existence of robust H∞ controller are presented in the form of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the proposed method.