The automatic seizure detection system can effectively help doctors to monitor and diagnose epilepsy thus reducing their workload. Many outstanding studies have given good results in the two-class seizure detection problems, but most of them are based on hand-wrought feature extraction. This study proposes an end-to-end automatic seizure detection system based on deep learning, which does not require heavy preprocessing on the EEG data or feature engineering. The fully convolutional network with three convolution blocks is first used to learn the expressive seizure characteristics from EEG data. Then these robust EEG features pertinent to seizures are presented as an input to the Nested Long Short-Term Memory (NLSTM) model to explore the inherent temporal dependencies in EEG signals. Lastly, the high-level features obtained from the NLSTM model are fed into the softmax layer to output predicted labels. The proposed method yields an accuracy range of 98.44-100% in 10 different experiments based on the Bonn University database. A larger EEG database is then used to evaluate the performance of the proposed method in real-life situations. The average sensitivity of 97.47%, specificity of 96.17%, and false detection rate of 0.487 per hour are yielded. For CHB-MIT Scalp EEG database, the proposed model also achieves a segment-level sensitivity of 94.07% with a false detection rate of 0.66 per hour. The excellent results obtained on three different EEG databases demonstrate that the proposed method has good robustness and generalization power under ideal and real-life conditions.