Atrial fibrillation (AF) is one of the most common arrhythmic complications. The diagnosis of AF usually requires long-term monitoring on the patient’s electrocardiogram (ECG) and then either having a domain expert examine the results, or extracting key features and then using a heuristic rule or data mining method to detect. Recently, researchers have attempted to use deep learning models, such as convolution neural networks (CNN) and/or Long Short-Term Memory (LSTM) neural networks to skip the feature extraction process and achieve good classification results. In this paper we propose a hybrid CNN-LSTM model which uses the short ECG signal from the PhysioNet/CinC Challenges 2017 dataset to explore and evaluate the relative performance of four data mining algorithms and three deep learning architectures, CNN, LSTM and CNN-LSTM. Our results show that all deep learning architectures except LSTM performed much better than machine learning algorithms without needing complicated feature extraction. CNN-LSTM is the best performer, achieving 97.08% accuracy, 95.52% sensitivity, 98.57% specificity, 98.46% precision, 0.99 AUC (Area under the ROC curve) value and 0.97 F1 score. With proper design of configuration, deep learning can be effective for automatic AF detection while data mining methods require domain knowledge and an extensive feature extraction and selection process to get satisfactory results.