Classification of EEG-based motor imagery (MI) is a crucial non-invasive application in brain-computer interface (BCI) research. This paper proposes a novel convolutional neural network (CNN) architecture for accurate and robust EEG-based MI classification that outperforms the state-of-the-art methods. The proposed CNN model, namely EEG-Inception, is built on the backbone of the Inception-Time network, which showed to be highly efficient and accurate for time-series classification. Also, the proposed network is an end-to-end classification, as it takes the raw EEG signals as the input and does not require complex EEG signal-preprocessing. Furthermore, this paper proposes a novel data augmentation method for EEG signals to enhance the accuracy, at least by 3%, and reduce overfitting with limited BCI datasets. The proposed model outperforms all the state-of-the-art methods by achieving the average accuracy of 88.4% and 88.6% on the 2008 BCI Competition IV 2a (four-classes) and 2b datasets (binary-classes), respectively. Furthermore, it takes less than 0.025 seconds to test a sample suitable for real-time processing. Moreover, the classification standard deviation for nine different subjects achieves the lowest value of 5.5 for the 2b dataset and 7.1 for the 2a dataset, which validates that the proposed method is highly robust. From the experiment results, it can be inferred that the EEG-Inception network exhibits a strong potential as a subject-independent classifier for EEG-based MI tasks.