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This paper considers the design problems of adaptive consensus protocol for nonlinear multiagent systems under directed topology and external disturbance. Considering external disturbance, we propose a new polynomial fuzzy modeling approach. Based on the monotonically increasing functions, novel centralized adaptive protocol and distributed consensus protocol are designed respectively to guarantee that all agents can reach agreement. The distributed protocol is independent of global information of network topology and thereby is fully distributed. By constructing Lyapunov functions, SOS-based relaxed sufficient criteria are presented to achieve consensus. In addition, the time-varying coupling weights approach finite steady-state values. A simulation example is provided to demonstrate the effectiveness of the proposed adaptive consensus techniques.