An 7.5 earthquake struck Palu in the northern coast of Sulawesi island, Indonesia, on 28 September 2018. Its focal mechanism was determined to be a left‐lateral strike‐slip fault, which is generally expected to not produce a tsunami. However, a large tsunami with runup heights of more than 6 m was observed along the coast of Palu city. Here, we show a complex triggering supershear source model as determined by teleseismic waveform inversion. Three asperities with different slip characteristics were found on the 120‐kilometer‐long rupture zone. Significant triggering rupture with a supershear speed was observed south of the epicenter, which was just beneath Palu city. This special rupture process can cause a strong directivity effect that produced anomalously large ground shaking with nonlinear effects in Palu area. The coseismic deformation determined from the inverted source model showed large horizontal displacements. These horizontal movements combined with complex bathymetry and topography could have pushed seawater to generate a tsunami even though the Palu earthquake was a strike‐slip event.