In this paper, we propose the design optimization of underlapped Si1-xGex-source tunneling field-effect transistors (TFETs) with a gate-all-around structure. The band-to-band tunneling rates, tunneling barrier widths, I-V transfer characteristics, threshold voltages, on/off current ratios, and subthreshold swings (SSs) were analyzed by varying the Ge mole fraction of the Si1-xGex source using a commercial device simulator. In particular, a Si0.2Ge0.8-source TFET among our proposed TFETs exhibits an on/off current ratio of approximately 1013, and SS of 27.4 mV/dec.