© 2020 Elsevier Ltd In this paper, the problem of non-fragile guaranteed-performance H∞ leader-following consensus protocol design for high-order multi-agent systems with Lipschitz nonlinearities and switching topologies is investigated. The communication interactions among all agents are described by a set of switching directed graphs, whose union contains a directed spanning tree rooting at the leader node. By constructing a nonsingular transformation, leader-following consensus of the concerned multi-agent system is transformed into the problem of asymptotic stability analysis for some consensus error systems. Taking into account the existences of exogenous disturbances in practical agent systems and gain perturbations in physical controller implementations, the non-fragile H∞ criterion is introduced not only to design the consensus protocol which is capable of tolerating some level of parametric uncertainties, but also to make the consensus error system asymptotically stable with a prescribed H∞ disturbance attenuation level. To regulate the consensus performance, a quadratic function collecting consensus errors among in-neighboring agents is proposed. By employing tools from algebraic graph theory and Lyapunov functional technique, sufficient conditions on the desired consensus protocol design are derived in terms of linear matrix inequalities. Simulation illustrates the effectiveness of the theoretical results.