In this paper, we propose a SiGe grating coupler to realize vertical coupling between the single-mode fiber and the SiGe on-chip device. To improve the coupling efficiency of the SiGe grating, we adopted a metal layer as the reflecting mirror on the chip backside, and we optimized the structure, including the etch depth, etch groove width, and grating period, using the finite-different time-domain method. We computed the grating coupling efficiency by analyzing the power and electric field distribution with and without the metal reflective layer. The simulation results show that the maximum coupling efficiency of the uniform grating is increased by 9.4 dB compared with the case without a metal layer, and its directionality is significantly improved. The maximum coupling efficiency of the SiGe grating obtained by simulation optimization is -1.34 dB at 1466 nm. Furthermore, we simulated and designed a two-step apodized grating based on the uniform grating, which further increased the maximum coupling efficiency by 0.55 dB compared with the uniform. Additionally, we performed a tolerance analysis on the coupled grating, including the thickness of the metal layer, the refractive index of the SiGe material, and the size of the grating. The analysis results show that the SiGe grating has a high tolerance for process deviations. Also, we fabricated a SiGe coupling grating, and the test results show that the maximum coupling efficiency of -2.7 dB is obtained at 1465 nm.