It is difficult to identify optimal cut-off frequencies for filters used with the common spatial pattern (CSP) method in motor imagery (MI)-based brain-computer interfaces (BCIs). Most current studies choose filter cut-frequencies based on experience or intuition, resulting in sub-optimal use of MI-related spectral information in the electroencephalography (EEG). To improve information utilization, we propose a SincNet-based hybrid neural network (SHNN) for MI-based BCIs. First, raw EEG is segmented into different time windows and mapped into the CSP feature space. Then, SincNets are used as filter bank band-pass filters to automatically filter the data. Next, we used squeeze-and-excitation modules to learn a sparse representation of the filtered data. The resulting sparse data were fed into convolutional neural networks to learn deep feature representations. Finally, these deep features were fed into a gated recurrent unit module to seek sequential relations, and a fully connected layer was used for classification. We used the BCI competition IV datasets 2a and 2b to verify the effectiveness of our SHNN method. The mean classification accuracies (kappa values) of our SHNN method are 0.7426 (0.6648) on dataset 2a and 0.8349 (0.6697) on dataset 2b, respectively. The statistical test results demonstrate that our SHNN can significantly outperform other state-of-the-art methods on these datasets.