During one of the stops, it was carrying 3820 passengers.
The Celebrity Solstice has visited a few times, most recently in January when it had 2926 guests.
The Diamond Princess, with 2850 passengers, docked last month, and again two weeks later, and the Oosterdam - with 1750 passengers - was in town in November.
Cunard, which operates the Queen Elizabeth, will send another of its ships - the Queen Mary 2 - to circumnavigate the country next month.
A Cunard spokeswoman said cruising was booming. "Latest official industry figures show that almost 60,000 New Zealanders took a cruise in 2013 - a 23 per cent increase on the previous year, and a new record."
As for Queen Elizabeth, today will be its fifth visit to New Zealand since 2011.
Raewyn Tan, of Cruise NZ, projected an increase in cruise customers for the 2015/16 year as firms are building bigger ships. "No one is building smaller ships, because the return on investment is just not there any more.
"Even when you're looking at the boutique end, they're also getting bigger."
That meant more passengers and more visitors to New Zealand.
"It's going to grow about 24 per cent in passengers in the 2015/16 year as the ships continue to get bigger and bigger."
Ms Tan warned that if Auckland's port wasn't expanded some time over the next five years, there would be dire consequences for the local tourism industry.