For a brain-computer interface (BCI) system, a calibration procedure is required for each individual user before he/she can use the BCI. This procedure requires approximately 20-30 min to collect enough data to build a reliable decoder. It is, therefore, an interesting topic to build a calibration-free, or subject-independent, BCI. In this article, we construct a large motor imagery (MI)-based electroencephalography (EEG) database and propose a subject-independent framework based on deep convolutional neural networks (CNNs). The database is composed of 54 subjects performing the left- and right-hand MI on two different days, resulting in 21 600 trials for the MI task. In our framework, we formulated the discriminative feature representation as a combination of the spectral-spatial input embedding the diversity of the EEG signals, as well as a feature representation learned from the CNN through a fusion technique that integrates a variety of discriminative brain signal patterns. To generate spectral-spatial inputs, we first consider the discriminative frequency bands in an information-theoretic observation model that measures the power of the features in two classes. From discriminative frequency bands, spectral-spatial inputs that include the unique characteristics of brain signal patterns are generated and then transformed into a covariance matrix as the input to the CNN. In the process of feature representations, spectral-spatial inputs are individually trained through the CNN and then combined by a concatenation fusion technique. In this article, we demonstrate that the classification accuracy of our subject-independent (or calibration-free) model outperforms that of subject-dependent models using various methods [common spatial pattern (CSP), common spatiospectral pattern (CSSP), filter bank CSP (FBCSP), and Bayesian spatio-spectral filter optimization (BSSFO)].