Heart disease remains one of the leading causes of mortality worldwide, highlighting the need for accurate and efficient computer-aided diagnostic methods. Although machine learning has shown considerable potential for heart disease prediction, the presence of redundant and irrelevant clinical features often limits classification performance and model interpretability. This study proposes a wrapper-based feature selection framework that integrates Particle Swarm Optimization (PSO) with the Random Forest (RF) classifier for heart disease classification using the Heart Disease UCI dataset. The proposed framework applies data preprocessing, including missing value imputation, categorical encoding, feature scaling, and binary target transformation, followed by PSO-based feature selection and Random Forest classification. Experimental results demonstrate that the proposed PSO-RF framework reduces feature dimensionality while improving predictive performance compared with the baseline Random Forest model. The optimized model achieved an accuracy of 88.59% with an AUC of 0.9279, indicating its effectiveness in identifying the most informative clinical attributes and enhancing classification capability. The novelty of this study lies in the systematic integration of wrapper-based PSO feature selection with Random Forest under a unified evaluation framework, providing an effective balance between predictive accuracy and model simplicity. These findings demonstrate the potential of the proposed approach to support intelligent clinical decision-support systems by improving diagnostic reliability while reducing computational complexity in cardiovascular disease prediction.