We report measurements of the Diffuse Galactic Light (DGL) spectrum in the near-infrared, spanning the wavelength range 0.95-1.65 {mu}m by the Cosmic Infrared Background ExpeRiment (CIBER). Using the low-resolution spectrometer (LRS) calibrated for absolute spectro-photometry, we acquired long-slit spectral images of the total diffuse sky brightness towards four high-latitude fields spread over four sounding rocket flights. To separate the DGL spectrum from the total sky brightness, we correlated the spectral images with a 100 {mu}m intensity map, which traces the dust column density in optically thin regions. The measured DGL spectrum shows no resolved features and is consistent with other DGL measurements in the optical and at near-infrared wavelengths longer than 1.8 {mu}m. Our result implies that the continuum is consistently reproduced by models of scattered starlight in the Rayleigh scattering regime with a few large grains.