"We are nowhere near the pre-pandemic levels," said Griffiths, adding that Dubai had weathered the storm better than many other airports.
"I think it's quite gratifying that for the eighth year in succession we are still the world's busiest international airport, so that's a very good statistic," he said.
"It means that although our figures aren't what we would like them to be, other airports have clearly fared a lot worse than we have."
Passenger figures collapsed to 25.9 million in 2020, a drop of 70 per cent, when Dubai airport was closed from March to July and fleets were grounded around the world.
More than a third of last year's passengers flew in the final quarter, when travel restrictions eased and Dubai opened its Expo 2020 world exhibition and hosted the Dubai airshow, the world's first since the pandemic.
This year, the airport is projecting 57 million passengers but is hoping to exceed the target, Griffiths said.
"Fifty-seven is our projection for 2022, but if current growth rates continue, I hope we'll smash through that target and we expect I think by the end of 2023 to be much closer to the pre-pandemic levels," he said.
He said an easing of restrictions in the Asia-Pacific region, where Australia reopened its borders to vaccinated tourists this week, would fuel the recovery.
"The slow recovery in some of the transport markets because of the restrictions, particularly in Australasia and Asia... as they start to fall away, the transport traffic through Dubai will surge ahead and we will see a recovery which we believe will be very strong," Griffiths said.
"However what I would say is that the current growth rates that we've seen and the recovery in all the major markets is incredibly strong."
India remained the top destination from Dubai with 4.2 million passengers, followed by Pakistan, Saudi Arabia and Britain, while the number of flight movements rose 28.1 per cent year-on-year to 233,375.