We propose a taper-underlaid spot-size converter (TU-SSC) with an offset which consists of two vertically stacked taper layers. The designed TU-SSC reduces coupling loss of a high index-contrast waveguide with $1.5%{Delta}$ to a single mode fiber from 1.5 dB to 0.27 dB. We also considered the effects of mask misalignment in the fabrication process of TU-SSC, and optimized the design of TU-SSC so that the additional loss of TU-SSC for the mask misalignment of $3{mu}m$ in the photo-lithography process was as low as 0.13 dB.