In this paper, the reconstruction error between the real system to be controlled and its T-S fuzzy model is considered, and fuzzy approximator is employed to cope with the reconstruction error. As a result, it reaches an adaptive controller that has two parts: one is obtained by solving certain linear matrix inequalities (LMIs) (fixed part) and another one is acquired by the fuzzy approximator in which the related parameters are tuned by adaptive law (variable part). The proposed controller can guarantee the control state to converge and uniformly bounded while maintaining all the signals involved stable. Also, the convergence in terms of relaxing the LMIs conservatism is discussed. An inverted pendulum is provided to demonstrate the effectiveness of the proposed adaptive fuzzy controller.