Direct-injection spark-ignition (DISI) engines have high thermal efficiency; however, they also show high soot emissions under cold-start conditions. It is also well-known that fuel-injection timing has a significant effect upon soot emissions, and that such emissions increase when fuel is injected during the early intake and latter compression strokes. In design calculations, it is important to reproduce this characteristic profile of soot emissions, what we call the bathtub-type profile. In this study, we performed numerical calculations of soot emissions from a DISI engine under cold-start conditions by using a compact-size soot-formation model previously proposed by authors. As results, it was shown that the proposed model reproduces the bathtub-type profile well. Furthermore, by changing the model of the HACA mechanism and adjusting the model coefficient, the quantitative reproducibility of soot emission was improved while maintaining the bathtub-type profile.