We simulate the strong ground motion of 1999 Chi-Chi, Taiwan earthquake (Mw = 7.6) by considering a three-dimensional source rupture model in a full waveform three-dimensional wave propagation study. The strong ground motion records during the 1999 Chi-Chi earthquake show various characteristics at different sites in Taiwan. We adopt a three-dimensional source model derived from an inversion study with identical path effects as considered in this three-dimensional forward study. Comparisons between the simulation results and observed waveforms from dense island-wide strong motion stations demonstrate that the fault geometry, lateral velocity variation, and complex source rupture process greatly influence the distribution of strong ground shaking. The simulation has reproduced the heavy damage area that is mainly concentrated in the hanging wall, especially close to the surface break of the Chelungpu fault. The source directivity effect is also reproduced and shows serious shaking along the northward rupture direction. Low-velocity material in the shallow part of the Western Plain is found to generate significantly amplified ground motions. In the Central Range, the shaking is relatively weak owing to the energy radiation characteristics of a low-angle thrust of the Chelungpu faulting system. The wavefield is then amplified by a high-velocity gradient under the Coastal Range. Our simulation results in the frequency range of 0.01-0.5 Hz give good agreement with the extensive strong motion observations of the Chi-Chi earthquake. We find that adequate source representation, good three-dimensional crustal velocity structures, and careful numerical work are necessary to make the ground motion prediction feasible.