At a celebrity-studded event in New York on Tuesday, Parker announced the launch of Airtime, which allows users to host video chats with their Facebook friends, or find someone new to talk to based on similar interests.
Airtime has been described as "Chatroulette without the nudity", in reference to the open video network that was notorious as a place to see people in various states of undress.
Airtime provides a "fun and safe" place for people to log in using their Facebook account and then be connected via video chat to others.
The new network accesses information on public Facebook profiles and then searches for people the user may know, are nearby, are friends of friends or have common interests.
There are options to narrow the search using a series of metrics, or hide any interests that the user does not want the system to search on.
Alongside one-on-one video chats, users can also pull in favourite YouTube videos, or videos already shared on Facebook to watch with others.
In a blog post, the Airtime team said: "Airtime is not just a product, it's a network service designed to create live shared experiences online, between two sets of people: those that you know and those who you want to know.
"Airtime is the most efficient, easy to use, browser-based video chat service between friends using their existing Facebook networks.
"The service allows you to share live experiences through content, and expand beyond your social graph to discover new people through similar interests in an environment that is collaborative, fun and safe."
Parker, who was played by Justin Timberlake in Facebook movie The Social Network, feels that modern social networking on sites such as Facebook, of which he owns a stake valued at $2.65bn, has reduced interactions to impersonal clicks and updates.
In an interview with TechCrunch last year, Parker said that Airtime would help people escape the "rigid and constraining" structure of existing social networks, and create a place to bring people together based on common interests.
He has reunited with Shawn Fanning, his co-founder of notorious music file-sharing site Napster, to launch Airtime. Parker will be chairman of the firm and Fanning chief executive.
After building up its user base, Airtime is planning a number of revenue streams, including selling advertising or potentially virtual goods.
Speaking at the launch event, Fanning and Parker said that the broader adoption of webcams and faster internet connections means that the time is right for a new video chat service.
They said that automatic "abuse prevention" filters were included in the site to avoid the type of lewd behaviour that became synonymous with the likes of Chatroulette. Anyone who violates the site's terms of service will have their accounts blocked.