We present the near- and mid-infrared zodiacal light spectrum obtained with the AKARI Infra-Red Camera (IRC). A catalog of 278 spectra of the diffuse sky covering a wide range of Galactic and ecliptic latitudes was constructed. The wavelength range of this catalog is 1.8-5.3 {mu}m with wavelength resolution of lambda /Delta lambda ~20. Advanced reduction methods specialized for the slit spectroscopy of diffuse sky spectra are developed for constructing the spectral catalog. Based on the comparison analysis of the spectra collected in different seasons and ecliptic latitudes, we confirmed that the spectral shape of the scattered component and the thermal emission component of the zodiacal light in our wavelength range does not show any dependence on location and time, but relative brightness between them varies with location. We also confirmed that the color temperature of the zodiacal emission at 3-5 {mu}m is 300+/-10 K at any ecliptic latitude. This emission is expected to be originated from sub-micron dust particles in the interplanetary space.