Delta saw its revenue grow 6% to $47 billion last year.
"Demand for travel continues to grow faster than anything we've seen over the last few years," said Bastian said in an interview with The Atlanta Journal-Constitution.
He said Delta's operational performance -- in areas such as on-time performance and baggage handling -- is producing loyal customers and causing more people to choose Delta.
The airline's revenue growth allowed it to inch ahead of American Airlines, which has for several years been the world's largest airline in revenue and other measures after merging with US Airways in 2013.
Delta got a benefit last year due to the fact that it does not fly the Boeing 737 Max, which was grounded last year after two fatal plane crashes. American, United and Southwest had to cancel flights due to the grounding, and Delta picked up some of the traffic.
That trend could reverse when the 737 Max returns to service, which is expected later this year.
But Bastian said he thinks Delta got only a "marginal benefit" from the Max grounding.
By other measures such as flight capacity, fleet size and employee counts, United or American are still larger.
“It’s far more important to be the best, but if you’re the best and the largest it’s great,” Bastian said. “Scale matters in this business.... I do think it’s sustainable.”
Delta said its pre-tax income of $6.2 billion for 2019 was its best in history.
But the company struggled during the year with rising costs, as it allocated more to pay for $1.6 billion in employee profit sharing and pensions, quickly scaled up its operations and struggled to handle a bigger-than-ever summer rush with overtime and other measures.
“These are some costs to help us stay ahead of the growth,” Bastian said.