On 26 November 1999, at 1321 UT, central Vanuatu was struck by a large offshore earthquake (Mw 7.5) followed by a tsunami that killed five people and caused significant damage to nearshore structures, mainly at Martelli Bay, south Pentecost Island. The tsunami is simulated using the Geowave model. The Tsunami Open and Progressive Initial Conditions System (TOPICS) source component of the model simulates the initial water column deformation, and the propagation and runup are simulated with the FUNWAVE fully nonlinear Boussinesq and dispersive model. A special effort was made on the construction of the computational grid through comprehensive bathymetry data sets obtained especially from two multibeam bathymetric surveys performed after the earthquake and tsunami. Three different tsunami sources have been considered. The first one is the fault rupture itself, the second is a landslide located east of Ambrym Island, and the third source is a submarine structure within the Selwyn Strait that will be considered as a landslide, however, with a large uncertainty because it could be a result of lava deposit as well. It is found that the earthquake-derived tsunami source fits most of the postsurvey observations, in particular the overall wave amplitudes (up to 6--7 m observed and simulated). The timing of the tsunami is also satisfactory when objective interpretation of the eyewitnesses is processed. Thus it is found that the hypothetical landslide-derived tsunami contributions are not necessary to predict the tsunami. This is because they do not help in the tsunami timing but also because their wave amplitude contributions are one order of magnitude lower than that of the earthquake source.