Integrating the graded index (GRIN) waveguide with the 2-D inversely-tapered waveguide, a new design of spot size converter (SSC) has been proposed to couple the light beam between the cleaved single-mode fiber (SMF) and the silicon (Si) wire waveguide on the silicon-on-insulator (SOI) platform. The device demonstrates a low coupling loss of 0.27 dB when it is coupled to a cleaved SMF. The polarization-dependent loss (PDL) is less than 0.25 dB, and the 1-dB alignment tolerance is about −2.0~2.0 µm for both vertical and horizontal directions. At the same time, the starting tip width of the tapered waveguide is kept at the level of the lithography limitation at the current commercial silicon photonics fab. This integrated SSC could be an improved design for reducing the coupling loss between the cleaved SMF and the Si waveguide.