In recent decades, heart disease threatens people’s health seriously because of its prevalence and high risk of death. Therefore, predicting heart disease through some simple physical indicators obtained from the regular physical examination at an early stage has become a valuable subject. Clinically, it is essential to be sensitive to these indicators related to heart disease to make predictions and provide a reliable basis for further diagnosis. However, the large amount of data makes manual analysis and prediction taxing and arduous. Our research aims to predict heart disease both accurately and quickly through various indicators of the body. In this paper, a novel heart disease prediction model is given. We propose a heart disease prediction algorithm that combines the embedded feature selection method and deep neural networks. This embedded feature selection method is based on the LinearSVC algorithm, using the L1 norm as a penalty item to choose a subset of features significantly associated with heart disease. These features are fed into the deep neural network we built. The weight of the network is initialized with the He initializer to prevent gradient varnishing or explosion so that the predictor can have a better performance. Our model is tested on the heart disease dataset obtained from Kaggle. Some indicators including accuracy, recall, precision, and F1-score are calculated to evaluate the predictor, and the results show that our model achieves 98.56%, 99.35%, 97.84%, and 0.983, respectively, and the average AUC score of the model reaches 0.983, confirming that the method we proposed is efficient and reliable for predicting heart disease.