Peloton is well-positioned to dominate the at-home fitness category because there are few serious competitors, Wedbush analyst James Hardiman told CNBC on Wednesday.

"Very few of the many alternatives that are out there really rose to the level of being a legitimate threat to Peloton," Hardiman said on "Closing Bell," referencing survey work his firm conducted for a recent client note.

In that note Tuesday, Wedbush initiated coverage of Peloton with an outperform rating while placing a $37 price target on the stock. It represents a roughly 25% increase from where shares of Peloton closed Tuesday.

The stock was up around 2% on Wednesday, trading around $30. It notched an intraday high of $31.44.

The only real threat to Peloton, Hardiman said, was SoulCycle, which has hinted at launching an at-home fitness bike of its own.

"That's one that we've got our eyes on," Hardiman said of SoulCycle.

The main principle underlying Wedbush's upgrade is a belief that Peloton will not "prove to be a fad, but instead one of a small number of fitness companies likely to be an enduring force going forward," Hardiman and his colleagues wrote.

To that end, they argue Peloton could reach about 4 million subscribers globally, with about 3 million of them living in the U.S.

"There's a significant portion of people that don't own the product that are interested in the product," Hardiman told CNBC. "And then among actual Peloton owners, satisfaction was through the roof. Ninety-seven percent of people were satisfied based on the work we did."

The Wedbush analysts acknowledge the "considerable work" Peloton has to expand its products and its reach, but they suggest the company has "the best shot of becoming synonymous with at-home fitness, an undeniable trend with considerable runway."

Hardiman wrote in the note that Peloton's short-term growth will be powered by exercise bike sales, but argues its subscriptions will be its main value driver over the long-term.

Peloton was a pioneer with its cycles and treadmills that are equipped with screens for users to join live and recorded fitness classes remotely.

Peloton went public in late September in a closely watched initial public stock offering, but its stock opened more than 11% below its initial pricing of $29 per share.

Some of Peloton's detractors point to the price of its products and classes. Its cycles cost nearly $2,000 and treadmills are $4,000. A full membership is $39 per month, and a monthly digital option costs $12.99.

CEO and co-founder John Foley acknowledged that criticism in a CNBC interview just ahead of the company's IPO.

"Our wish is to get the price down and, in the coming years, we want to make sure tens of millions of people around the globe are able to afford a Peloton bike and Peloton [treadmill]," Foley said.

The company more recently took heat for a holiday TV advertisement, which some argued contained elements of sexism and classism, but the controversy was not viewed as a long-term detriment to the company.

Peloton hit an all-time high of $37.02 on Dec. 2, and its market cap is around $8.7 billion.