On February 6, 2018, a damaging earthquake with a magnitude of 6.4 on the moment magnitude scale occurred off the eastern coast of Taiwan near Hualien, causing the collapse of buildings and human casualties. About 17 seconds after the occurrence of the earthquake, an earthquake alarm was issued by the earthquake early warning (EEW) system operated by the Central Weather Bureau of Taiwan (CWB). During the Hualien earthquake sequence (including foreshocks, mainshock, and aftershocks), the EEW system sent 44 warnings without any false alarms. However, one earthquake with magnitude larger than 5.0 was missed by the EEW system because the multiple earthquakes occurred in a short period causing the EEW system to be unable to correctly distinguish multiple P-wave arrivals. In this study, we proposed an approach that instead uses the centroid of the triggered stations as an effective epicenter and then accordingly calculates magnitude and intensity. The proposed method has been implemented in the new EEW system and was tested during the period of the Hualien earthquake sequence. The results show that the proposed method can shorten the processing time by an average of 4.7 seconds as compared to the existing EEW system and can detect all large events without being affected by the multiple concurrent events. In addition, the predicted intensities from the new EEW system were similar to the original intensities.