Knowledge of water in the solar system is important for the understanding of a wide range of evolutionary processes and the thermal history of the solar system. To explore the existence of water in the solar system, it is indispensable to investigate hydrated minerals and/or water ice on asteroids. These water-related materials show absorption features in the 3um band (wavelengths from 2.7 to 3.1um). We conducted a spectroscopic survey of asteroids in the 3um band using the Infrared Camera (IRC) on board the Japanese infrared satellite AKARI. In the warm mission period of AKARI, 147 pointed observations were performed for 66 asteroids in the grism mode for wavelengths from 2.5 to 5um. According to these observations, most C-complex asteroids have clear absorption features (>10% with respect to the continuum) related to hydrated minerals at a peak wavelength of approximately 2.75um, while S-complex asteroids have no significant features in this wavelength range. The present data are released to the public as the Asteroid Catalog using AKARI Spectroscopic Observations (AcuA-spec).