To address the issue of unknown False Data Injection (FDI) attacks on controllers in DC microgrids, a distributed secondary controller for DC microgrids based on a linear extended state observer is presented to ensure that the system can achieve the control objectives of voltage regulation and current sharing even when subjected to FDI attacks. Firstly, the secondary control problem of multi-bus DC microgrids with FDI attacks is transformed into a first-order Multi-Agent System(MAS) fault-tolerant consistency problem, and the impact of FDI attacks on the microgrid system is analyzed. Then, a Linear Extended State Observer(LESO) is employed to detect the estimated injected FDI attack signals. Furthermore, a fault-tolerant secondary controller is designed to eliminate the adverse effects of FDI attacks on the system. The stability of the proposed method is verified using a Lyapunov function. Finally, the effectiveness and superiority of the proposed control method are experimentally demonstrated.