Fraud detection in banking systems is crucial for financial stability, customer protection, and regulatory compliance. Machine learning plays a vital role in enhancing data analysis and real-time fraud detection. Feature selection is an essential phase in machine learning to improve credit card fraud detection. By eliminating the negative impact of redundant and irrelevant features and selecting effective ones, feature selection aids the classification phase in machine learning. This paper presents an effective method based on a hybrid Grey Wolf and Cheetah algorithm to enhance the accurate identification of fraudulent credit card transactions by recognizing relevant features. Additionally, in the machine learning classification phase, the Support Vector Machine (SVM) method is employed, which has been improved through parameter tuning using the hybrid Grey Wolf and Cheetah algorithm. The results demonstrate that the proposed method has achieved at least a 1% improvement in fraud detection on the Australian credit dataset compared to other methods.