The mathematical properties of high-dimensional (HD) spaces show remarkable agreement with behaviors controlled by the brain. Computing with HD vectors, referred to as “hypervectors,” is a brain-inspired alternative to computing with numbers. HD computing is characterized by generality, scalability, robustness, and fast learning, making it a prime candidate for utilization in application domains such as brain–computer interfaces. We describe the use of HD computing to classify electroencephalography (EEG) error-related potentials for noninvasive brain–computer interfaces. Our algorithm naturally encodes neural activity recorded from 64 EEG electrodes to a single temporal–spatial hypervector without requiring any electrode selection process. This hypervector represents the event of interest, can be analyzed to identify the most discriminative electrodes, and is used for recognition of the subject’s intentions. Using the full set of training trials, HD computing achieves on average 5% higher single-trial classification accuracy compared to a conventional machine learning method on this task (74.5% vs. 69.5%) and offers further advantages: (1) Our algorithm learns fast: using only 34% of training trials it achieves an average accuracy of 70.5%, surpassing the conventional method. (2) Conventional method requires prior domain expert knowledge, or a separate process, to carefully select a subset of electrodes for a subsequent preprocessor and classifier, whereas our algorithm blindly uses all 64 electrodes, tolerates noises in data, and the resulting hypervector is intrinsically clustered into HD space; in addition, most preprocessing of the electrode signal can be eliminated while maintaining an average accuracy of 71.7%.