Based on the coherent population trapping theory, a new physical model of the electromagnetically induced grating (EIG) is proposed. Analytical expression of the dielectric susceptibility is derived using this model. Owing to the atomic coherence, introduced by the coherent population trapping, three regions of dielectric susceptibility, i.e., a gain region, a region with no absorption and high-refraction index, and a dark region, are formed. Based on this model and the energy level of 87Rb, a novel scheme to implement the diffraction grating is proposed. Moreover, theoretical analysis and calculation of this grating are carried out. The results show that in the region with no absorption and high refractive index, the grating presents a pure phase grating and the first-order diffraction intensity can reach 0.4. In the gain region, however, the grating is a combination of phase grating and amplitude grating, and at its largest-gain point, the maximum of the first-order diffraction efficiency arrives at 1.26, and the second-order diffraction efficiency can also increase to 0.31.