The carrier, which is rebuilding after being pushed to the bring last year by the Covid crisis, cited the easing of travel restrictions and higher rates of vaccination against Covid-19 for the uptick in demand.
Norwegian carried nearly 700,000 passengers in July, up 50% year-on-year, and operated 33 aircraft – around 50% more than it did in June.
It said the number of aircraft and routes it operates would "gradually be increased to meet market demand" during autumn and winter.
During the pandemic, Norwegian has axed its long-haul operation completely, including operations at its Gatwick base, and re-focused its attentions on almost exclusively flying domestic routes after a protracted restructure, which was finally completed in May.
Load factor in July was 74.4%, up seven percentage points year-on-year, with Norwegian noting travel to northern Norway, in particular, had been "especially popular" during the summer.
Chief executive Geir Karlsen said the carrier was enjoying a long overdue "time of optimism". "In July, we received the highest number of bookings since the society closed down in March last year," he said.
"Our customers have been aware of the exceptional circumstances and have been well prepared to meet rules and requirements for both domestic and international travel.
"We are pleased that the booking figures are increasing again, and it is great to see that many of our colleagues are back at work.
"Even though the pandemic is not yet over, we are experiencing a time of optimism which is great after such a long period of high uncertainty."