In federated learning systems, malicious attackers can manipulate training datasets by injecting backdoor triggers to achieve data poisoning. Addressing this vulnerability, this paper proposes a new defense method, the adaptive differential privacy stochastic gradient descent (ADP-SGD) algorithm, which increases the Euclidean distance between malicious and benign updates to enhance aggregation efficiency. Experiments were conducted on typical datasets, and the results show that combining ADP-SGD with the m-Krum aggregation algorithm can effectively defend against backdoor attacks in complex attack environments. While ensuring the accuracy of the main task, it significantly reduces the success rate of backdoor attacks, especially under the condition of unknown proportions of malicious participants, proving to be effective and robust.