The cluster formation problem of the multi-agent system in the presence of disturbances and unmodelled uncertainties has been studied. Agents in the system are partitioned into multiple clusters and each cluster is required to maintain a predefined time-varying sub-formation, where the sub-formations can be different from each other. An identifier-based robust control algorithm using the neighbouring relative information has been proposed to accomplish the time-varying cluster formation. Some sufficient conditions for the second-order multi-agent system to achieve the control objective have been proposed based on the graph theory and the Lyapunov method. Numerical simulations are provided to testify the validity of the algorithm. Compared to the previous work on cluster formation control, the novel feature of this study is that disturbances and unmodelled uncertainties are taken into consideration and the authors propose a robust cluster formation control algorithm based on a non-linear identifier to eliminate the adverse effects of disturbances and unmodelled uncertainties.