Objective: Epileptic seizure prediction based on scalp electroencephalogram (EEG) is of great significance for improving the quality of life of patients with epilepsy. In recent years, a number of studies based on deep learning methods have been proposed to address this issue and achieve excellent performance. However, most studies on epileptic seizure prediction by EEG fail to take full advantage of temporal-spatial multi-scale features of EEG signals, while EEG signals carry information in multiple temporal and spatial scales. To this end, in this study, we proposed an end-to-end framework by using a temporal-spatial multi-scale convolutional neural network with dilated convolutions for patient-specific seizure prediction. Methods: Specifically, the model divides the EEG processing pipeline into two stages: the temporal multi-scale stage and the spatial multi-scale stage. In each stage, we firstly extract the multi-scale features along the corresponding dimension. A dilated convolution block is then conducted on these features to expand our model’s receptive fields further and systematically aggregate global information. Furthermore, we adopt a feature-weighted fusion strategy based on an attention mechanism to achieve better feature fusion and eliminate redundancy in the dilated convolution block. Results: The proposed model obtains an average sensitivity of 93.3%, an average false prediction rate of 0.007 per hour, and an average proportion of time-in-warning of 6.3% testing in 16 patients from the CHB-MIT dataset with the leave-one-out method. Conclusion: Our model achieves superior performance in comparison to state-of-the-art methods, providing a promising solution for EEG-based seizure prediction.