Two-dimensional apodized grating couplers are proposed with grating grooves realized by a series of nano-rectangles, with the feasibility of digital tailoring the equivalent refractive index of each groove in order to obtain the Gaussian output diffractive mode in order to enhance the coupling efficiency to the optical fiber. According to the requirement of leakage factor distribution for a Gaussian output profile, the corresponding effective refractive index of the grating groove, duty cycle, and period are designed according to the equivalent medium theory. The peak coupling efficiency of 93.1% at 1550 nm and 3 dB bandwidth of 82 nm are achieved.