Southwest Airlines Chief Marketing Officer Ryan Green told CNBC that his airline won't make passengers who don't want to fly on the Boeing 737 Max pay additional airfare to switch flights.

Southwest does not charge passengers a fee to change their tickets, but it does usually charge customers the difference in airfare.

All Boeing 737 Max airliners have been grounded since March 13, with the jet pulled from Southwest's flight schedule until August 5.

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Those who don't want to the fly on the Boeing 737 Max won't have to. According to Southwest Airlines Chief Marketing Officer Ryan Green, passengers who find themselves booked on a 737 Max flight will be allowed to switch flights free of charge.

"If they're uneasy about flying on a Max aircraft, we'll be flexible with them," Green told CNBC. "We'll be understanding of that and allow them to fly on a different flight without paying any difference in fare."

The Dallas, Texas-based low-cost carrier does not charge passengers a fee to change their tickets, but it does charge customers the difference in airfare. But in the case of concerns around the Max, an exception will be made.

Read more: American Airlines CEO reveals when he would feel safe flying on the Boeing 737 Max again.

All 371 Boeing 737 Max airliners in service around the world have been grounded since March 13 following the crashes of Ethiopian Airlines Flight ET302 and Lion Air Flight JT610. Southwest Airlines is the largest operator of the Boeing 737 Max, with a fleet of 34 aircraft. All 34 planes, which are in desert storage in Victorville, California, have been pulled from the flight schedule until at least August 5. However, in a recent statement, Southwest CEO Gary Kelly said the company does not have a confirmed timeline for the 737 Max's return to service.

Southwest's concerns about passengers who may not want to fly on the 737 Max are reasonable. A poll conducted by Business Insider a week after the Ethiopian Airlines crash showed that 53% of American adults surveyed would not want to fly on a Boeing 737 Max, even after the Federal Aviation Administration clears the aircraft for service.