This catalog contains the 278 low-resolution (R~20) near-infrared (1.8-5.3micron) spectra of diffuse sky covering a wide range of galactic and ecliptic latitudes with the Infrared Camera (IRC) on board AKARI before the exhaustion of liquid-helium (from September 2006 to May 2007). Advanced reduction methods specialized for the slit spectroscopy of diffuse sky spectra are developed for constructing this spectral catalog. Filter wheel of the IRC instrument has dark position to measure the dark current, and uncertainty due to dark current subtraction is estimated to be <3nW/m2/sr at 2micron (Tsumura & Wada, 2011PASJ...63..755T). Point sources brighter than mK(Vega)=19 were detected on the slit and masked for deriving the diffuse spectrum. It was confirmed that the brightness due to unresolved galactic stars under this detection limit is negligible (<0.5% of the sky brightness at 2.2 micron) by a Milky Way star count model (TRILEGAL; Girardi et al., 2005A&A...436..895G). Cumulative brightness contributed by unresolved galaxies can be estimated by the deep galaxy counts, being <4nW/m2/sr at K band in the case of limiting magnitude of mK=19 (Keenan et al., 2010ApJ...723...40K).