This study tackles the output consensus problem for a class of nonlinear two-dimensional (2-D) multi agent systems that do complex tasks repetitively in a finite domain via iterative learning control (ILC). The aim is to design a distributed adaptive learning consensus tracking control strategy that enables all 2-D multi agents to achieve the task of consensus tracking control under nonrepetitive conditions, even if only a part of the agents can detect the reference surface. An adaptive parameter, which adjusted by the tracking errors of the agent itself and the neighbor agents in the last iteration, is designed to approximate the unknown varying parameter of the nonlinear 2-D agent. Then, based on the approximated parameter and the iteration-varying reference surfaces, the distributed adaptive learning consensus tracking control strategy is obtained and the convergence of the output consensus tracking control is proved. In the end, simulations are presented to verify the effectiveness of the investigated distributed adaptive learning consensus tracking control for 2-D multi agent system with random variations on initial boundary and reference surface.