"Everybody is usually so mad when a new iPhone launches because they are so excited about the new technology and all the great things, but not a lot of people can get it because they are under contract with their traditional carrier," Claure said in a CNBC "Squawk Box" interview.
With the plan, Sprint customers can exchange their old iPhones for new models at any time for $15 month, Claure added.
Claure also said the exchanges make sense from a business standpoint because iPhones retain much of their resale value. "There is a huge market for used iPhones. Not a lot of people can afford a $700 phone, but if you get an iPhone today, nobody will know it's used."
The company announced the plan last month.
Claure also discussed Moody's credit downgrade of the company, saying it caught them offguard. "We respect what they have to say, and we're focused on the turnaround of Sprint."
Sprint shares have dropped more than 7 percent in September and over 30 percent in the last 12 months.