In order to solve the problem of consensus tracking in the given time interval for non-affine nonlinear multi-agent systems, a distributed consensus tracking control algorithm is designed based on an iterative learning control method. A communication topology of multi-agent systems is firstly composed of an introduced virtual leader and all followers, where the role of the virtual leader is to provide the desired trajectory, and then the iterative learning consensus tracking controller for each follower is constructed by using the tracking error of each followerand its neighbors under the condition that only some followers can obtain leader information. At the same time, the non-affine nonlinear multi-agent systems are transformed into affine forms using the mean value theorem, and the convergence of the proposed algorithm is proved based on the contraction mapping method, and thus the convergence conditions of the algorithm are given. Theoretical analysis shows that when the nonlinear function of the agent is unknown, the proposed algorithm can make the non-affine nonlinear multi-agent systems achieve consistent tracking gradually with the increase of iterations in the given time interval. Finally, a simulation example is given to further verify the effectiveness of the proposed algorithm.