The study of primitive asteroids is relevant to understanding the origin and evolution of our Solar System. These asteroids contain valuable information about volatile and organic compounds present during the prebiotic stages of Earth and other terrestrial planets. Interest in the main-belt asteroids that are the likely sources of primitive near-Earth asteroids (NEAs) has increased in anticipation of the two sample-return missions that reached their targets in 2018 and will bring samples to Earth within a few years. Concurrently, the discovery of water ice on the surfaces of two primitive asteroids (24 Themis and 65 Cybele) placed the focus on the outer-belt, where more asteroids could harbor water ice on, or below the surface. In 2010 we started our PRIMitive Asteroids Spectroscopic Survey (PRIMASS) with the goal of studying the surface of primitive asteroids at different locations in the main belt, by means of visible and near-infrared spectroscopy. Here we present PRIMASS-L, a spectral library that contains the results of PRIMASS. As of July 2018, this library gathers spectra of about 500 asteroids from 10 families and two dynamical groups of asteroids that had been sparsely studied before. PRIMASS uses a variety of ground-based facilities, including the 3.0-m NASA Infrared Telescope Facility (IRTF) on Mauna Kea (Hawai, USA) and the 4.1-m Southern Astrophysical Research Telescope (SOAR, participated by NOAO), at Cerro Pachón (Chile). We also use the 10.4-m Gran Telescopio Canarias (GTC), and the 3.6m Telescopio Nazionale Galileo (TNG), both located at the El Roque de Los Muchachos Observatory (ORM, La Palma, Spain) and the 3.6m New Technology Telescope (NTT), located at la Silla Observatory. This survey is on-going and aims to contain a thounsand of spectra by 2019. Making PRIMASS-L publicly available at the Small Bodies Node of the Planetary Data System (SBN-PDS, NASA) will enable synergies with other data sets containing physical parameters (e.g. polarymetric properties and geometric albedo) and family affiliation. This will push the characterization of the families and of primitive material to a new level and improve our understanding of the evolution of our Solar System and other planetary systems.