Heart Disease or Cardiovascular diseases (CVDs) are a group of disorders of the heart and blood vessels including coronary heart disease, cerebrovascular disease, rheumatic heart disease and others. It is the number one cause of death globally, taking an estimated 17.9 million lives each year, and one third of these deaths occur in people under 70 years of age, which is working groups. The prevalence and the expense of treating heart disease had projected to increase in many countries by 2030. In the last decades, many researches had conducted on heart disease to minimize deaths caused due to these diseases. However, heart disease remains as the number one cause of death globally. Therefore, it is very essential to conduct a study that initiates alternative means to diagnose heart diseases. Accordingly, this study aims to bring new insight by combining Self Organizing Neural Network (SONN) and Support Vector machine (SVM) algorithms on different kernel functions to classify heart diseases. In this research, we used 303 clinical datasets collected from Cleveland Clinic Foundation. These datasets had pre-processed to make it useful for the experimentation and we conducted all the experimentations by using Python on PyCharm IDE. First, we experimented and evaluated the dataset by using SVM alone on different kernel functions. Then we experimented by combining SONN and SVM algorithms. To combine these two algorithms, first SONN used to get the cluster representation of each input variables, then these clusters fed to the SVM as a feature to classify Heart disease. Evaluations on the combined model showed that SONN has increased the accuracy and specificity of SVM on Polynomial Kernel function to diagnose Heart disease. Keywords: Heart Disease, Support Vector Machine, Self-Organizing Neural Network, Kohonen Self-Organizing Map, Machine Learning