We present an analysis of the ultraluminous X-ray source (ULX) population in 75 Virgo cluster late-type galaxies, including all those with a star formation rate ≳1 M_⊙ yr^−1 and a representative sample of the less star forming ones. This study is based on 110 observations obtained over 20 yr with the Chandra X-ray Observatory Advanced Camera for Imaging Spectroscopy. As part of a Large Chandra Program, new observations were obtained for 52 of these 75 galaxies. The data are complete to a sensitivity of ≈10^39 erg s^−1, with a typical detection limit of ≈3 × 10^38 erg s^−1 for the majority of the sources. The catalogue contains about 80 ULXs (0.3–10 keV luminosity >10^39 erg s^−1), and provides their location, observed flux, de-absorbed luminosity, and (for the 25 most luminous ones) simple X-ray spectral properties. We discuss the ULX luminosity function in relation to the mass and star formation rate of the sample galaxies. We show that recent models of low-mass plus high-mass X-ray binary populations (scaling with stellar mass and star formation rate, respectively) are mostly consistent with our observational results. We tentatively identify the most luminous X-ray source in the sample (a source in IC 3322A with L_X ≈ 6 × 10^40 erg s^−1) as a recent supernova or its young remnant. The properties of the sample galaxies (morphologies, stellar masses, star formation rates, total X-ray luminosities from their point-source population) are also summarized.