The electroencephalogram (EEG) signal is a medium to realize a brain-computer interface (BCI) system due to its zero clinical risk and portable acquisition devices. Current EEG-based BCI research usually requires a subject-specific adaptation step before a BCI can be employed by a new user. In contrast, the subject-independent scenario, where a well trained model can be directly applied to new users without precalibration, is particularly desired. Considering this critical gap, the focus in this letter is developing an effective EEG signal analysis adaptively applied to subject-independent settings. We present a convolutional recurrent attention model (CRAM) that utilizes a convolutional neural network to encode the high-level representation of EEG signals and a recurrent attention mechanism to explore the temporal dynamics of the EEG signals as well as to focus on the most discriminative temporal periods. Extensive experiments on a benchmark multiclass EEG dataset containing four movement intentions indicate that the proposed model is capable of exploiting the underlying invariant EEG patterns across different subjects and generalizing the patterns to new subjects with better performance than a series of state-of-the-art and baseline approaches by at least eight percentage points. The implementation code is made publicly available.¹¹https://github.com/dalinzhang/CRAM.