The Hubble Source Catalog (HSC) combines lists of sources detected on images obtained with the WFPC2, ACS and WFC3 instruments aboard the Hubble Space Telescope (HST) and now available in the Hubble Legacy Archive. The catalogue contains time-domain information for about two million of its sources detected using the same instrument and filter on at least five HST visits. The Hubble Catalog of Variables (HCV) aims to identify HSC sources showing significant brightness variations. A magnitude-dependent threshold in the median absolute deviation of photometric measurements (an outlier-resistant measure of light-curve scatter) is adopted as the variability detection statistic. It is supplemented with a cut in χred2 that removes sources with large photometric errors. A pre-processing procedure involving bad image identification, outlier rejection and computation of local magnitude zero-point corrections is applied to the HSC light-curves before computing the variability detection statistics. About 52 000 HSC sources have been identified as candidate variables, among which 7,800 show variability in more than one filter. Visual inspection suggests that ∼70% of the candidates detected in multiple filters are true variables, while the remaining ∼30% are sources with aperture photometry corrupted by blending, imaging artefacts or image processing anomalies. The candidate variables have AB magnitudes in the range 15–27m, with a median of 22m. Among them are the stars in our own and nearby galaxies, and active galactic nuclei.