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.