Aiming at privacy preservation, Federated Learning (FL) is an emerging machine learning approach enabling model training on decentralized devices or data sources. The learning mechanism of FL relies on aggregating parameter updates from individual clients. However, this process may pose a potential security risk due to the presence of malicious devices. Existing solutions are either costly due to the use of compute-intensive technology, or restrictive for reasons of strong assumptions such as the prior knowledge of the number of attackers and how they attack. Few methods consider both privacy constraints and uncertain attack scenarios. In this paper, we propose a robust FL approach based on the credibility management scheme, called Fed-Credit. Unlike previous studies, our approach does not require prior knowledge of the nodes and the data distribution. It maintains and employs a credibility set, which weighs the historical clients' contributions based on the similarity between the local models and global model, to adjust the global model update. The subtlety of Fed-Credit is that the time decay and attitudinal value factor are incorporated into the dynamic adjustment of the reputation weights and it boasts a computational complexity of O(n) (n is the number of the clients). We conducted extensive experiments on the MNIST and CIFAR-10 datasets under 5 types of attacks. The results exhibit superior accuracy and resilience against adversarial attacks, all while maintaining comparatively low computational complexity. Among these, on the Non-IID CIFAR-10 dataset, our algorithm exhibited performance enhancements of 19.5% and 14.5%, respectively, in comparison to the state-of-the-art algorithm when dealing with two types of data poisoning attacks.