Despite a moderate magnitude, Mw=6.4, the 02/05/2016 Meinong, Taiwan, earthquake caused significant damage in Tainan City and the surrounding areas. Several seismograms display an impulsive S-wave velocity pulse with an amplitude of about 1 m/s, which is similar to large S-wave pulses recorded for the past several larger damaging earthquakes, such as the 1995 Kobe, Japan, earthquake (Mw=6.9) and the 1994 Northridge, California, earthquake (Mw=6.7). The observed PGV in the Tainan area is about 10 times larger than the median PGV of Mw=6.4 crustal earthquakes in Taiwan. We investigate the cause of the localized strong ground motions. The peak-to-peak ground-motion displacement at the basin sites near Tainan is about 35 times larger than that at a mountain site with a similar epicentral distance. At some frequency bands (0.9 to 1.1 Hz), the amplitude ratio is as large as 200. Using the focal mechanism of this earthquake, typical “soft” and “hard” crustal structures, and directivity inferred from the observed waveforms and the slip distribution, we show that the combined effect yields an amplitude ratio of 17 to 34. The larger amplitude ratios at higher frequency bands can be probably due to the effects of complex 3-D basin structures. The result indicates that even from a moderate event, if these effects simultaneously work together toward amplifying ground motions, the extremely large ground motions as observed in Tainan can occur. Such occurrences should be taken into consideration in hazard mitigation measures in the place with frequent moderate earthquakes.