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In this paper, an observer-based robust adaptive fuzzy control strategy is presented for uncertain nonlinear dynamical systems subject to non-symmetric dead-zone nonlinearity. Within this scheme, fuzzy logic systems are used to estimate unknown nonlinear function of the dynamic system and unknown upper bounds of unmatched uncertainties, respectively. A state observer based on state variable filters is designed to estimate all the states which are not available for measurement in the system. Moreover, the adaptive scheme requires only the information about the bounds of the dead-zone slopes. By the Lyapunov function stability theorem, the asymptotical stability of the resulting closed-loop system can be guaranteed, and the output tracking performance of the whole system can be achieved. Finally, some simulation results are introduced to verify the effectiveness of the proposed controller.