“High Maintenance,” a web series on Vimeo about the many customers of a Brooklyn marijuana dealer, has won a devoted following and plenty of critical acclaim. Each of its first 13 episodes has been watched hundreds of thousands of times. The New Yorker raved that the show, “freed of the constraints” of formulas imposed by television schedules, radiates “new ideas about storytelling.”

But will viewers pay to watch it?

Vimeo, the video-sharing web service owned by IAC, will release three new episodes of “High Maintenance” on Tuesday. The new episodes — each less than 20 minutes long — are $2 apiece, or $8 for a set that includes three more that will be released in January. This is the first time that Vimeo has funded the series directly, and represents the company’s first push into original content, following a recent trend among larger digital companies such as Yahoo, Netflix and Amazon.

While Vimeo’s chief executive, Kerry Trainor, is betting that viewers will pay up, he says his ambitions go beyond generating a new source of revenue. He sees “High Maintenance” as the perfect show to be a foundation for a prestige television brand, and compares his site’s developing identity to that of premium cable in the 1970s, an analogy in which YouTube plays advertising-powered network television to Vimeo’s HBO.

“We really feel like Vimeo is in the world to find a higher-quality creator, delivering a different experience than what you’d typically find on YouTube,” Mr. Trainor said. “Not to say that YouTube is bad, but Vimeo on the whole has much more of a premium cable and even a film sensibility. That’s what tends to do well on the platform.”