In this paper, the band-gap characteristics of 3-D EBG structure composed of stratified orthogonal or non-orthogonal dielectric gratings are analyzed. Though the complete band-gap for electromagnetic waves with arbitrary polarization and arbitrary propagation direction does not exist, a common polarization-independent broad band-gap for the normal incidence is found. These structures can be used as the substrate of printed or low-profile antenna. The related curves of stop band-width vs. geometric and constitutive parameters, and also 3 dB stop bandwidth vs. the finite number of layer are provided as valuable reference data for the engineering design. It is found that the performance of the non-orthogonal gratings is better than the orthogonal one.