These days, heart disease comes to be one of the major health problems which have affected the lives of people in the whole world. Moreover, death due to heart disease is increasing day by day. So the heart disease prediction systems play an important role in the prevention of heart problems. Where these prediction systems assist doctors in making the right decision to diagnose heart disease easily. The existing prediction systems suffering from the high dimensionality problem of selected features that increase the prediction time and decrease the performance accuracy of the prediction due to many redundant or irrelevant features. Therefore, this paper aims to provide a solution of the dimensionality problem by proposing a new mixed model for heart disease prediction based on (Naïve Bayes method, and machine learning classifiers).In this study, we proposed a new heart disease prediction model (NB-SKDR) based on the Naïve Bayes algorithm (NB) and several machine learning techniques including Support Vector Machine, K-Nearest Neighbors, Decision Tree, and Random Forest. This prediction model consists of three main phases which include: preprocessing, feature selection, and classification. The main objective of this proposed model is to improve the performance of the prediction system and finding the best subset of features. This proposed approach uses the Naïve Bayes technique based on the Bayes theorem to select the best subset of features for the next classification phase, also to handle the high dimensionality problem by avoiding unnecessary features and select only the important ones in an attempt to improve the efficiency and accuracy of classifiers. This method is able to reduce the number of features from 13 to 6 which are (age, gender, blood pressure, fasting blood sugar, cholesterol, exercise induce engine) by determining the dependency between a set of attributes. The dependent attributes are the attributes in which an attribute depends on the other attribute in deciding the value of the class attribute. The dependency between attributes is measured by the conditional probability, which can be easily computed by Bayes theorem. Moreover, in the classification phase, the proposed system uses different classification algorithms such as (DT Decision Tree, RF Random Forest, SVM Support Vector machine, KNN Nearest Neighbors) as a classifiers for predicting whether a patient has heart disease or not. The model is trained and evaluated using the Cleveland Heart Disease database, which contains 13 features and 303 samples.Different algorithms use different rules for producing different representations of knowledge. So, the selection of algorithms to build our model is based on their performance. In this work, we applied and compared several classification algorithms which are (DT, SVM, RF, and KNN) to identify the best-suited algorithm to achieve high accuracy in the prediction of heart disease. After combining the Naive Bayes method with each one of these previous classifiers the performance of these combines algorithms is evaluated by different performance metrics such as (Specificity, Sensitivity, and Accuracy). Where the experimental results show that out of these four classification models, the combination between the Naive Bayes feature selection approach and the SVM RBF classifier can predict heart disease with the highest accuracy of 98%. Finally, the proposed approach is compared with another two systems which developed based on two different approaches in the feature selection step. The first system, based on the Genetic Algorithm (GA) technique, and the second uses the Principal Component Analysis (PCA) technique. Consequently, the comparison proved that the Naive Bayes selection approach of the proposed system is better than the GA and PCA approach in terms of prediction accuracy.