A conventional brain-computer interface (BCI) requires a complete data gathering, training, and calibration phase for each user before it can be used. In recent years, a number of subject-independent (SI) BCIs have been developed. Many of these methods yield a weaker performance compared to the subject-dependent (SD) approach, and some are computationally expensive. A potential real-world application would greatly benefit from a more accurate, compact, and computationally efficient subject-independent BCI. In this work, we propose a novel subject-independent BCI framework, named CCSPNet (Convolutional Common Spatial Pattern Network) that is trained on the motor imagery (MI) paradigm of a large-scale electroencephalography (EEG) signals database consisting of 400 trials for every 54 subjects who perform two-class hand-movement MI tasks. The proposed framework applies a wavelet kernel convolutional neural network (WKCNN) and a temporal convolutional neural network (TCNN) in order to represent and extract the spectral features of EEG signals. A common spatial pattern (CSP) algorithm is implemented for spatial feature extraction, and the number of CSP features is reduced by a dense neural network. Finally, the class label is determined by a linear discriminant analysis (LDA) classifier. The CCSPNet evaluation results show that it is possible to have a compact BCI that achieves both SD and SI state-of-the-art performance comparable to complex and computationally expensive models.