Two remarkable typhoon-induced traveling ionospheric disturbances (TIDs) with concentric and northwest-southeast (NW-SE) alignments, respectively, associated with concentric gravity waves (CGWs) and ionosphere instabilities possibly seeded by CGWs, were observed in total electron content (TEC) derived from ground-based Global Navigation Satellite System networks in Taiwan and Japan when the Category 5 Super Typhoon Nepartak approached Taiwan on 7 July 2016. The concentric TIDs (CTIDs) first appear with horizontal phase velocities of ~161–200 m/s, horizontal wavelengths of ~160–270 km, and periods of ~15–22 min during 08:00–11:20 UT. Following the CTIDs, the NW-SE aligned nighttime medium-scale TIDs (MSTIDs) are formed on the west edge of the CTIDs over the Taiwan Strait during 11:30–14:00 UT. It is suggested that the MSTIDs are produced by the electrodynamical coupling of Perkins instability and CGW-induced polarization electric fields. This study proposes connections of typhoon-induced CTIDs and subsequently occurring MSTIDs in the low-latitude ionosphere.