A tsunami wave will leave evidence of erosion and deposition in coastal lakes, making it possible to determine the runup height and when it occurred. Here, we use four lakes now located at elevations of 19–91 m a.s.l. close to the settlement of Saqqaq, West Greenland, to show that at least two giant tsunamis occurred 7300–7600 years ago with runup heights larger than 40 m. We infer that any tsunamis from at least nine giga-scale landslides must have happened 8500–10 000 years ago.