This study presents strong ground motion simulation methods for the future fragility study of a power plant in Southern Taiwan. The modified stochastic method and empirical Green function method are utilized to synthesize the strong ground motions of specific events. A modified physical random function model of strong ground motions for specific sites and events is presented in this study with verification of sample level. Based on the special models of the source, path, and local site, the random variables of the physical random function of strong ground motions is obtained. The inverse Fourier transform is used to simulate strong ground motions. For the empirical Green function method, the observed site records from small earthquake events occurring around the source area of a large earthquake are collected to simulate the broadband strong ground motion from a large earthquake event. Finally, an application of proposed two simulated methods of this study for simulating the ground motion records of Nishi-Akashi Station at 1995 Kobe earthquake and 2006 Southern Taiwan PingDong earthquake are presented.