A prompt diagnosis of breast cancer in its earliest phases is necessary for effective treatment. While Computer-Aided Diagnosis systems play a crucial role in automated mammography image processing, interpretation, grading, and early detection of breast cancer, existing approaches face limitations in achieving optimal accuracy. This study addresses these limitations by hybridizing the improved quantum-inspired binary Grey Wolf Optimizer with the Support Vector Machines Radial Basis Function Kernel. This hybrid approach aims to enhance the accuracy of breast cancer classification by determining the optimal Support Vector Machine parameters. The motivation for this hybridization lies in the need for improved classification performance compared to existing optimizers such as Particle Swarm Optimization and Genetic Algorithm. Evaluate the efficacy of the proposed IQI-BGWO-SVM approach on the MIAS dataset, considering various metric parameters, including accuracy, sensitivity, and specificity. Furthermore, the application of IQI-BGWO-SVM for feature selection will be explored, and the results will be compared. Experimental findings demonstrate that the suggested IQI-BGWO-SVM technique outperforms state-of-the-art classification methods on the MIAS dataset, with a resulting mean accuracy, sensitivity, and specificity of 99.25%, 98.96%, and 100%, respectively, using a tenfold cross-validation datasets partition.