Plane-wave pseudopotential total energy method was used to calculate the effects of impurity Li atom on crystal structure, electronic and dielectric properties of Si2N2O. It is proved that Li atom prefers to occupy interstitial site than to substitute the Si atomic site. In addition, the presence of interstitial Li atom leads to relaxation of internal coordinates of Si, N, and O atoms, and bring out a different X-ray diffraction (XRD) pattern compared with that of a pure Si2N2O. The result is helpful to understand the diversity of experimental XRD data for Si2N2O sintered with and without Li2O additive. The theoretical polycrystalline dielectric constant of Li-doped Si2N2O is larger than that of a pure one, which can be attributed to a reduction of band gap. The mechanism is that interstitial Li atom provides extra electronic states at the bottom of conductive band.