This article describes a citizen-science project conducted by the Spanish Virtual Observatory (SVO) to improve the orbits of near-Earth asteroids (NEAs) using data from astronomical archives. The list of NEAs maintained at the Minor Planet Center (MPC) is checked daily to identify new objects or changes in the orbital parameters of already catalogued objects. Using NEODyS we compute the position and magnitude of these objects at the observing epochs of the 938 046 images comprising the Eigth Data Release of the Sloan Digitised Sky Survey (SDSS). If the object lies within the image boundaries and the magnitude is brighter than the limiting magnitude, then the associated image is visually inspected by the projects collaborators (the citizens) to confirm or discard the presence of the NEA. If confirmed, accurate coordinates and, sometimes, magnitudes are submitted to the MPC. Using this methodology, 3,226 registered users have made during the first fifteen months of the project more than 167,000 measurements which have improved the orbital elements of 551 NEAs (6% of the total number of this type of asteroids). Even more remarkable is the fact that these results have been obtained at zero cost to telescope time as NEAs were serendipitously observed while the survey was being carried out. This demonstrates the enormous scientific potential hidden in astronomical archives. The great reception of the project as well as the results obtained makes it a valuable and reliable tool for improving the orbital parameters of near-Earth asteroids.