Sleep apnea is one of the most common sleep disorders in the world. It is a common problem for patients to suffer from sleep disturbances. In this paper, we propose a deep convolutional neural network (CNN) model based on the oxygen saturation (SpO2) signal from a smart sensor. This is the reason why we called ZleepNet a network for sleep apnea detection. The proposed model includes three convolutional layers, which include ReLu activation function, 2 dense layers, and one dropout layer for predicting sleep apnea. In this proposed model, the use of signals for detecting the sleep apnea can be reduced from 25 sensors to 1 sensor. We conducted experiments to evaluate the performance of the proposed CNN using real patient data and compared them with traditional machine learning methods such as least discriminant analysis (LDA) and support vector machine (SVM), baggy representation tree, and artificial neural network (ANN) on publicly available sleep datasets using the same parameter setting. The results show that the proposed model outperformed the other methods with the accuracy of 91.30% with the split rate of 0.2% in which the training data are 20% and testing data are 80%. The accuracy of the proposed CNN is 90.33% when compared with the LDA which achieved 86.5% accuracy with the split rate of 0.5% in which training data are 50% and testing data are 50%. It achieved 91.56% accuracy when compared with the support vector machine (SVM) in which training data are 70% and testing data are 30%. The achieved accuracy of the proposed CNN is 91.89% when compared with bagging representation tree in which training data are 90% and testing data are 10%. The accuracy of the proposed CNN is 91.30% in which training data are 83% and testing data are 17% when compared with artificial neural networks (ANN).