This paper aims to design and implement an automatic heart disease diagnosis system using MATLAB. The Cleveland data set for heart diseases was used as the main database for training and testing the developed system. In order to train and test the Cleveland data set, two systems were developed. The first system is based on the Multilayer Perceptron (MLP) structure on the Artificial Neural Network (ANN), whereas the second system is based on the Adaptive Neuro-Fuzzy Inference Systems (ANFIS) approach. Each system has two main modules, namely, training and testing, where 80% and 20% of the Cleveland data set were randomly selected for training and testing purposes respectively. Each system also has an additional module known as case-based module, where the user has to input values for 13 required attributes as specified by the Cleveland data set, in order to test the status of the patient whether heart disease is present or absent from that particular patient. In addition, the effects of different values for important parameters were investigated in the ANN-based and Neuro-Fuzzy-based systems in order to select the best parameters that obtain the highest performance. Based on the experimental work, it is clear that the Neuro-Fuzzy system outperforms the ANN system using the training data set, where the accuracy for each system was 100% and 90.74%, respectively. However, using the testing data set, it is clear that the ANN system outperforms the Neuro-Fuzzy system, where the best accuracy for each system was 87.04% and 75.93%, respectively.