A noise-robust data-driven formation control strategy with noisy data for leader-follower multi-agent systems (MASs) is investigated. The formation control is achieved through the integration of the data-driven control and the consensus control under model-free conditions. In contrast to traditional formation control approaches that depend on precise dynamics models, the complex model identification is eliminated in the proposed method by using the system input-output data. Moreover, the history data considered in this paper contains bounded noise. The data matrixces of the system are constructed from history data of MASs, and the necessary and sufficient conditions for the data-driven formation control are provided. Based on the history data, a distributed formation control protocol is designed to enable agents to achieve the desired formation while utilizing only local neighbor information. Numerical simulations are provided to demonstrate the effectiveness of the proposed strategy.