An unusual devastating tsunami occurred on 28 September 2018 after a strike-slip faulting earthquake in Sulawesi, Indonesia. The induced tsunami struck Palu city with 4-m wave height and flow depth. We performed a two-step analysis to investigate the source of the tsunami. We first conducted the teleseismic source inversion and obtained the slip distribution of the strike-slip fault. Our tsunami simulation from the coseismic deformation of the seismically-estimated strike-slip faulting produced a tsunami comparable to the leading part of the observation at Pantoloan. We then jointly utilized the tsunami waveform and Synthetic Aperture Radar (SAR) data to reconstruct the detailed slip distribution on the fault plane. Because of the lack of SAR data in the bay, the tsunami data is necessary to constrain the offshore slip distribution, which directly induces the tsunami. The inverted source model shows a strike-slip fault which consists of three segments extending from the epicenter to the south of 1.4°S with two bends and two asperities around Palu city. The joint inversion model accurately reconstructs the observed surface displacements and the leading part of the tsunami waveform. Our result exhibits the significant contribution of the strike-slip faulting to the tsunami, but it also suggests additional tsunami sources, such as landslides, for the high inundations near Palu bay. The result also indicates that regional devastating tsunamis can result from an onshore strike-slip fault with localized large dip slip.