Cardiac arrhythmia is a typically clinical manifestation of cardiovascular disease which leads to serious health problem. Detection of arrhythmia is traditionally relying on manual interpretation of electrocardiography (ECG) signals by cardiologists, which is time consuming and subjective. Therefore, development of an automated arrhythmia detection system with high accuracy becomes urgent in clinical applications. In the present study, we propose an effective deep learning model with one-lead ECG signals to automatically detect different types of arrhythmias based upon tunable Q-factor wavelet transform (TQWT) and complete ensemble empirical mode decomposition (CEEMD). First, TQWT decomposes the ECG signal into different frequency bands by using the input parameters (Q, R, and J) without any segmentation, which are used to extract the main subband with majority of the ECG signal’s energy. Second, CEEMD is used to decompose the main subband of ECG signals into different intrinsic modes. It captures most part of the main subband’s information, preserving important waveform features as a slightly asymmetry. It is employed to measure the variability of ECG signals. There is no need for the preprocessing of QRS detection. Then, they are selected as features and fed to combined neural networks consisting of one-dimensional (1D) convolutional neural networks (CNN) and long short-term memory (LSTM) networks for multi-class classification of cardiac arrhythmias. Finally, experiments are carried out on the well-known and publicly available MIT-BIH arrhythmia database to evaluate the performance of the proposed method, in which 744 ECG signal fragments for one lead (MLII) of seventeen classes of heart beats from 29 persons were extracted. By using 10-fold cross-validation style, the achieved average classification accuracy is reported to be 97.20%, 96.85%, 96.48% and 96.13%, respectively, for five-class, thirteen-class, fifteen-class and seventeen-class classification. Compared with other state-of-the-art methods, the results demonstrate superior performance and the proposed method has the potential to serve as a candidate for the automatic detection of myocardial dysfunction in the clinical ECG examination.