Accurate prediction of cardiovascular disease (CVD) is essential for timely intervention and improved patient outcomes. This paper presents a hybrid model, BPSO-RAF-CNN that integrates Binary Particle Swarm Optimization (BPSO) with a Regularized Accuracy-Based Fitness Function (RAF) and a Convolutional Neural Network (CNN) to improve prediction performance through optimized feature selection. The approach begins with feature engineering on cardiovascular data, followed by BPSO-RAF to identify the most important, predictively salient and compact feature subset, lowering dimensionality and improving generalization. These selected features are then fed into a CNN for final classification. Extensive experiments demonstrate that BPSO-RAF-CNN outperforms traditional classifiers (Logistic Regression, SVM, Naive Bayes, Decision Tree, Random Forest) achieving an accuracy of 87.05%, Precision 89.71%, Recall 83.77%, F1-score of 86.05%. And Specificity 90.22%, all with a standard deviation 0.5%. The model also shows good performance across 10-fold cross-validation, indicating strong generalization.