A man shows AirPods Pro at an Apple store on East Nanjing Road on October 30, 2019 in Shanghai, China. Apple's new AirPods Pro with active noise cancellation are on sale on October 30 in China.

Sales of Apple's AirPods nearly doubled to $6 billion this year and should take another leap forward next year, according to Toni Sacconaghi of Bernstein.

The analyst said in a note Friday that Apple could sell 85 million AirPods in 2020, generating about $15 billion in revenue. If sales of the wireless headphones grew at the same rate again in 2021, the product would become Apple's third largest business, Sacconaghi said.

Sacconaghi, who has a market perform rating on Apple's stock, is consistently rated as the top investor for IT hardware and electronics manufacturing services by Institutional Investor magazine.

AirPods Pro are already sold out in Apple Stores and at many online retailers for the holiday season, with some selling AirPods on eBay for large premiums. The Pro is sold for $249 on Apple's website, while the regular AirPods start at $159.

However, the AirPod's run may be short-lived, said Sacconaghi, who compared the product's trajectory to the iPad's rapidly slowing growth four years after it launched. As more iPhone users buy AirPods, there are fewer potential customers, according to Sacconaghi.

"Given AirPods' extraordinarily steep adoption curve and rapid saturation of the iPhone installed base, we see a dramatic deceleration in AirPods revenue growth by 2021 or 22, to single digit growth rates or possibly lower," Sacconaghi wrote.