<p>This study presents a new optimization technique, the three-term conjugate gradient method, which enhances the efficiency of solving unconstrained optimization problems and its application in training artificial neural networks to predict heart diseases. It incorporates a gradient condition and a modified gradient difference vector. The method is validated through its global convergence and sufficient condition, ensuring both mathematical accuracy and computational stability. Compared to traditional conjugate gradient methods and three-term conjugate gradient methods, the proposed method demonstrates superior performance, characterized by fewer iterations, reduced function evaluations, and lower computational time. The method is also used to teach artificial neural networks how to predict heart disease, with an 88.15% success rate and precision, recall, and F1-Score values of 0.87, 0.86, and 0.87, respectively. These results confirm the method’s effectiveness in enhancing the predictive power of artificial neural networks making it a valuable tool for clinical applications. This study underscores the potential of the new method to improve decision-support systems in healthcare, aiding early detection and better patient outcomes. Future research may focus on refining the method and integrating it with other machine learning techniques to create advanced real-time predictive systems that further advance intelligent healthcare solutions.</p>