According to the airline, forward bookings and demand continue to show a "positive increase" as a greater number of markets unlock and ease restrictions.
Last month, the carrier flew 225,509 passengers, which, according to Norwegian, is around 100% more than June 2020.
Compared with last year, the total capacity for June reportedly increased by 182% with passenger traffic up 102%.
Geir Karlsen, chief executive of Norwegian, said the airline has seen a continued month-on-month increase in bookings.