A triggered communication mechanism-based adaptive control strategy is proposed for output consensus of a class of uncertain nonlinear multi-agent systems. A distributed estimator is constructed via intermittent communication with their own neighbours. This estimator provides desired trajectory for parts of followers who are not able to access to leader's information directly. Recursive sliding-modes and nonlinear gain functions are applied for performance improvement of traditional dynamic surface control approaches. Also, an adaptive parameter is introduced for neural networks' weights, and it is for simplification of computational complexity in our control strategy. In theory, it is proven that all signals in the multi-agent system are ultimately bounded, that consensus tracking errors converge to a neighbourhood around the origin, and that there exists Zeno-free behaviour. Three simulation examples validate the effectiveness of the proposed strategy.