Ground motions from normal-faulting earthquakes are generally considered to be smaller than those of strike-slip and thrust events. On 11 April 2011 a crustal normal-faulting earthquake [the Fukushima earthquake (M_w 6.6)] occurred in Eastern Japan. The peak ground acceleration (PGA) observed was considerably higher than the predictions of several ground-motion prediction equations (GMPEs), which were derived mainly from thrust or strike-slip earthquakes. In northeast Taiwan, the tectonic structure of the Ryukyu Arc and the Okinawa Trough typically entail normal-faulting earthquakes. Because of the normal-faulting earthquakes relevance to ground motions and nuclear power plant sites in northeast Taiwan, we evaluated the impact of the ground motion of normal-faulting earthquakes in offshore northeast Taiwan using a newly constructed attenuation relationship for PGA and pseudo-spectral acceleration (Sa). We collected 832 records from 13 normal-faulting earthquakes with focal depths of less than 50 km. The moment magnitude (M_w) of the 13 events was between 4 - 6. The Sa and PGA of normal-faulting earthquakes offshore northeast Taiwan determined with the newly constructed attenuation relationship were higher and lower, respectively, than those obtained using attenuation equations commonly used in the Taiwan subduction zone.