Observational study on near-infrared (IR) scattering properties of interstellar dust grains has been limited due to its faintness. Using all-sky maps obtained from Diffuse Infrared Background Experiment (DIRBE), we investigate the scattering property from diffuse Galactic light (DGL) measurements at 1.25, 2.2, and 3.5 {mu}m in addition to our recent analyses of diffuse near-IR emission (Sano et al. 2015; Sano et al. 2016). As a result, we first find that the intensity ratios of near-IR DGL to 100 {mu}m emission increase toward low Galactic latitudes at 1.25 and 2.2 {mu}m. The derived latitude dependence can be reproduced by a scattered light model of interstellar dust with a large scattering asymmetry factor g = <cos{theta}> of $0.8^{+0.2}_{-0.3}$ at 1.25 and 2.2 {mu}m, assuming an infinite Galaxy disk as an illuminating source. The derived asymmetry factor is comparable to the values obtained in the optical, but several times larger than that expected from a recent dust model. Since possible latitude dependence of ultraviolet-excited dust emission at 1.25 and 2.2 {mu}m would reduce the large asymmetry factor to the reasonable value, our result may indicate the first detection of such an additional emission component in the diffuse interstellar medium.