In this paper, we explored the local tsunami hazards induced by an active local seismic Quanzhou fault, along the coastlines of the City of Putian, Fujian Province, in the southeast of China. The simulation results indicated that the tsunami wave will hit the nearest coast of Putian 0.5 h after the earthquake occurs. The most serious tsunami inundation depth in Putian was less than 3.0 m. This study also conducted a sensitivity test of the tsunami amplitude and inundation in response to different seismic source parameters, particularly the rake and strike angles of the Quanzhou fault. Based on the post-earthquake survey and the most updated geophysical data, the uniform dislocation distribution is applied in the range of scientific geometrical characteristic parameters for numerical modeling. A 20° change in the rake angle increases the inundation area from 50.0 km2 to more than 100.0 km2, and increases the tsunami amplitude from 0.2 m to 1.0 m. In this study, the tsunami hazard of Putian is more sensitive to the rake than to the strike angle for a local fault. Tsunamis generated by seismic fault could also result in serious coastal flooding along the coastlines locally, and the time for emergency response is limited. The research results could provide technical support for refining local tsunami hazard assessment and contingency plans, to save decision-making time and avoid waste of social resources.