For a class of partially irregular multi-agent systems with arbitrary initial state, an iterative learning control algorithm is proposed. The method transforms formation control of multi-agent systems with fixed topology into a tracking problem in a broader sense, i.e., a leader firstly tracks a given desired trajectory, and then followers one-by-one track a certain agent by maintaining predetermined formation at all times, and this agent is seen as its own leader. At the same time, initial state of each agent is designed by the iterative learning law, in order to make each agent cruise formation in an arbitrary initial state according to expected formation. Moreover, the convergence condition of the algorithm is strictly proved in the theory, as well as the sufficient condition of the convergence condition in the sense of norm is given. The algorithm can realize stable formation of the multi-agent systems in arbitrary initial state in the limited time for all agents. Finally, the effectiveness of the proposed algorithm is further verified by the simulation example.