Unsupervised domain adaptation methods have made significant progress in the field of machine fault diagnosis. However, these methods generally assume the accessibility of source domain data during the cross-domain transfer phase. In practice, this assumption is often impractical due to data privacy requirements and the burden of data transmission and storage. Additionally, a key challenge lies in preventing the forgetting of source domain knowledge while performing cross-domain diagnosis in a source-free scenario. To address these issues, this paper proposes an anti-forgetting source-free domain adaptation method for machine fault diagnosis. Specifically, a prototype-based pseudo-label generation strategy, combined with a nearest-neighbor constraint, is employed to deeply explore diagnosis information in the unlabeled target domain data. Then, a fast nuclear-norm maximization constraint is introduced to reduce the density of target domain samples near the classification boundary, thereby decreasing the probability of misdiagnosis. Furthermore, a weighted Fisher regularization is designed to retain the diagnosis information of healthy states inherent in the source domain, thus mitigating information forgetting. Finally, comprehensive experiments are conducted to validate the superiority of our method in source-free cross-domain diagnosis from multiple perspectives, while also demonstrating its anti- forgetting properties.