A well-developed numerical tsunami computation technique was applied to simulate historical tsunamis of the 1604 to 1978 period in the Taiwan region. The observed tsunami for the November 14, 1986 Hualien earthquake was examined to test the reliability of the numerical technique. Based on the occurrence of historical tsunamis, the Taiwan area is divided into five areas, namely Keelung, Hualien, Taitung, Tainan and Hsinchu. Due to the less than complete understanding of historical tsunami earthquakes, a simulation of historical tsunami in each area was made by considering the focal mechanisms of recent earthquakes in the vicinity. The empirical relationship of the moment magnitude and fault dimension was utilized for the computation of the synthetic tsunamis to obtain the relation between Mw and the maximum tsunami amplitudes of the first tsunami wave. The earthquake magnitude which was responsible for generating disaster tsunamis were then estimated. The obtained earthquake magnitudes from these simulations are comparable to those reported in historical literature. In addition to enhancing the understanding of the possible causes of historical tsunamis, the simulations made in this study also provide important information regarding the characteristics of tsunami waveforms in different regions. This information provide useful insight for the purposes of establishing tsunami warnings.