The detailed source rupture process of the M 7.3 event (April 16, 2016, 01:25, JST) of the 2016 Kumamoto, Japan, earthquakes was derived from strong-motion waveforms using multiple-time-window linear waveform inversion. Based on the observations of surface ruptures, the spatial distribution of aftershocks, and the geodetic data, a realistic curved fault model was developed for source-process analysis of this event. The seismic moment and maximum slip were estimated as 5.5 × 1019 Nm (M w 7.1) and 3.8 m, respectively. The source model of the M 7.3 event had two significant ruptures. One rupture propagated toward the northeastern shallow region at 4 s after rupture initiation and continued with large slips to approximately 16 s. This rupture caused a large slip region 10-30 km northeast of the hypocenter that reached the caldera of Mt. Aso. Another rupture propagated toward the surface from the hypocenter at 2-6 s and then propagated toward the northeast along the near surface at 6-10 s. A comparison with the result of using a single fault plane model demonstrated that the use of the curved fault model led to improved waveform fit at the stations south of the fault. The source process of the M 6.5 event (April 14, 2016, 21:26, JST) was also estimated. In the source model obtained for the M 6.5 event, the seismic moment was 1.7 × 10 18 Nm (M w 6.1), and the rupture with large slips propagated from the hypocenter to the surface along the north-northeast direction at 1-6 s. The results in this study are consistent with observations of the surface ruptures.