The exponential consensus issue is investigated for leader-following multiagent systems (MASs) based on nonlinear parabolic partial differential equations (PDEs) on a directed graph via intermittent boundary control (IBC) methods. On the one hand, when the system’s state is accessible, an IBC protocol is designed based on the transfer information generated by the agent’s communication with its neighbors and the information coupling at the boundary $x= l$ , and the sufficient conditions for exponential consensus of leader-following MASs are obtained. On the other hand, when the system’s state is not available completely, the agent’s state is estimated by the proposed observer, and the observer’s coupling information and the boundary coupling information of the agent are adopted to design an IBC protocol to solve the leader-following consensus issue. Finally, two numerical simulations are supplied to account for the obtained theoretical results.