© ESO 2015. Aims. We present three independent catalogs of point-sources extracted from SPIRE images at 250, 350, and 500 μm, acquired with the Herschel Space Observatory as a part of the Herschel Virgo Cluster Survey (HeViCS). The catalogs have been cross-correlated to consistently extract the photometry at SPIRE wavelengths for each object. Methods. Sources have been detected using an iterative loop. The source positions are determined by estimating the likelihood to be a real source for each peak on the maps, according to the criterion defined in the sourceExtractorSussextractor task. The flux densities are estimated using the sourceExtractorTimeline, a timeline-based point source fitter that also determines the fitting procedure with the width of the Gaussian that best reproduces the source considered. Afterwards, each source is subtracted from the maps, removing a Gaussian function in every position with the full width half maximum equal to that estimated in sourceExtractorTimeline. This procedure improves the robustness of our algorithm in terms of source identification. We calculate the completeness and the flux accuracy by injecting artificial sources in the timeline and estimate the reliability of the catalog using a permutation method. Results. The HeViCS catalogs contain about 52 000, 42 200, and 18 700 sources selected at 250, 350, and 500 μm above 3σ and are ∼75%, 62%, and 50% complete at flux densities of 20 mJy at 250, 350, 500 μm, respectively. We then measured source number counts at 250, 350, and 500 μm and compare them with previous data and semi-analytical models. We also cross-correlated the catalogs with the Sloan Digital Sky Survey to investigate the redshift distribution of the nearby sources. From this cross-correlation, we select ∼2000 sources with reliable fluxes and a high signal-to-noise ratio, finding an average redshift z ∼ 0.3 ± 0.22 and 0.25 (16-84 percentile). Conclusions. The number counts at 250, 350, and 500 μm show an increase in the slope below 200 mJy, indicating a strong evolution in number of density for galaxies at these fluxes. In general, models tend to overpredict the counts at brighter flux densities, underlying the importance of studying the Rayleigh-Jeans part of the spectral energy distribution to refine the theoretical recipes of the models. Our iterative method for source identification allowed the detection of a family of 500 μm sources that are not foreground objects belonging to Virgo and not found in other catalogs.