An efficient optical coupler to transfer the signal between an optical fiber and a silicon waveguide is essential for realizing the applications of silicon photonic integrated circuits such as optical communication and optical sensing. In this paper, we numerically demonstrate a two-dimensional grating coupler based on a silicon-on-insulator platform to obtain completely vertical and polarization-independent couplings, which potentially ease the difficulty of packaging and measurement of photonic integrated circuits. To mitigate the coupling loss induced by the second-order diffraction, two corner mirrors are respectively placed at the two orthogonal ends of the two-dimensional grating coupler to create appropriate interference conditions. Partial single-etch is assumed to form an asymmetric grating to obtain high directionalities without a bottom mirror. The two-dimensional grating coupler is optimized and verified with finite-difference time-domain simulations, achieving a high coupling efficiency of −1.53 dB and a low polarization-dependent loss of 0.015 dB when coupling to a standard single-mode fiber at approximately 1310 nm wavelength.