To address cluster consensus of discrete-time nonlinear multi-agent systems with unknown models under a fixed topology, this paper proposes a data-driven model-free adaptive control algorithm. Firstly, it is assumed that the system has a fixed topology, using the conception of pseudo partial derivative, the equivalent dynamic linearization model of the agent system is obtained. Under the consideration of the coupling coefficient among multiple agents, the cluster consensus error is proposed, and a data-driven cluster consensus control protocol is designed, then the convergence of tracking error is theoretically proved by using a compression mapping method, which shows that the proposed algorithm can complete the tracking task without the information of the agent model. Finally, the results are extended to multi-agent systems with a randomly switching topology. The effectiveness of the algorithm is verified by simulation examples.