This paper presents an automated patient-specific ECG classification algorithm, which integrates long short-term memory (LSTM) and convolutional neural networks (CNN). While LSTM extracts the temporal features, such as the heart rate variance (HRV) and beat-to-beat correlation from sequential heartbeats, CNN captures detailed morphological characteristics of the current heartbeat. To further improve the classification performance, adaptive segmentation and re-sampling are applied to align the heartbeats of different patients with various heart rates. In addition, a novel clustering method is proposed to identify the most representative patterns from the common training data. Evaluated on the MIT-BIH arrhythmia database, our algorithm shows the superior accuracy for both ventricular ectopic beats (VEB) and supraventricular ectopic beats (SVEB) recognition. In particular, the sensitivity and positive predictive rate for SVEB increase by more than 8.2% and 8.8%, respectively, compared with the prior works. Since our patient-specific classification does not require manual feature extraction, it is potentially applicable to embedded devices for automatic and accurate arrhythmia monitoring.