The recent advances in ECG sensor devices provide opportunities for user self-managed auto-diagnosis and monitoring services over the internet. This imposes the requirements for generic ECG classification methods that are inter-patient and device independent. In this paper, we present our work on using the densely connected convolutional neural network (DenseNet) and gated recurrent unit network (GRU) for addressing the inter-patient ECG classification problem. A deep learning model architecture is proposed and is evaluated using the MIT-BIH Arrhythmia and Supraventricular Databases. The results obtained show that without applying any complicated data pre-processing or feature engineering methods, both of our models have considerably outperformed the state-of-the-art performance for supraventricular (SVEB) and ventricular (VEB) arrhythmia classifications on the unseen testing dataset (with the F1 score improved from 51.08 to 61.25 for SVEB detection and from 88.59 to 89.75 for VEB detection respectively). As no patient-specific or device-specific information is used at the training stage in this work, it can be considered as a more generic approach for dealing with scenarios in which varieties of ECG signals are collected from different patients using different types of sensor devices.