We conducted tsunami numerical simulations around the Sulu Sea and the Celebes Sea using a modeling code called TUNAMI-N2. We investigated six scenarios for faults along the Negros Trench (2 segments), Sulu Trench (2 segments) and the Cotabato Trench (2 segments). We compared simulated results in numerical models based on a uniform grid in Cartesian coordinate system between using two bathymetry data, namely 1 arc-minute bathymetry data and 30 arc-second bathymetry data from GEBCO. The simulated results show that the maximum tsunami heights for simulations using 30 arc-second bathymetry data are mostly larger than those for simulations using 1 arc-minute bathymetry data. There is a threat of tsunami to the eastern coast of Sabah from an earthquake event of Mw 8.3 along the Sulu Trench with the maximum tsunami height of more than 1 m. Besides, Sabah may experience much smaller waves, of about less than 0.5 m for the tsunami source from the Negros Trench and the Cotabato Trench. This is because of two factors such as attenuation at wide shallow continental shelf and existence of small islands. The biggest maximum tsunami height at the Philippines coast is more than 4 m at Bayawan in case of the tsunami source from the Negros Trench. The tsunami arrives earlier for tsunami simulations using 30 arc-second bathymetry data than those using 1 arc-minute bathymetry data for all tide gauge stations except Lahad Datu, Tambisan, Bataraza and Bayawan. Detailed and accurate bathymetry data at shallower regions and near the coast are important to get reliable and much better results for tsunami computations.