A total of 2.8 million passengers used the airline last month, giving it a load factor of 90% and an increase of 1.2%.
Norwegian also reported a load factor of 96% following a 50% growth in passengers on its long haul routes.
In total, it operated 99.5% of scheduled flights in September with 79.6% departing on time.
Norwegian chief executive Bjorn Kjos said: “September’s figures show that our positive development continues across all markets, both with more passengers and a high load factor.
“It is also satisfying to see that more customers are choosing Norwegian when they are flying between the US and Europe and Europe and Asia.”