This study focuses on the asymptotical consensus and synchronisation for coupled uncertain parabolic partial differential equation (PDE) agents with Neumann boundary condition (or Dirichlet boundary condition) and subject to a distributed disturbance whose norm is bounded by a constant which is not known a priori. Based on adaptive distributed unit-vector control scheme and Lyapunov functional scheme, the distributed unit-vector controller with adaptive gain is suggested to provide for the leader–following tracking of uncertain parabolic PDE agents. The suggested gradient-based and mono-directional gain adaptation provides convergence without requiring the knowledge of an upper bound to the norm of the external disturbance. The simulation is proposed to account for the effectiveness and robustness of the provided method.