Virgin is attempting to gain control of the domain richardbranson.xxx.
The company took the action after an individual unconnected with the company registered the name.
"We have a complaint against the owner of richardbranson.xxx," a Virgin spokesman said.
The top-level domain launched last year after considerable debate. Virgin said it was spending an increasing amount of time protecting its brands, including the Branson name, online.
In order to win control of the domain Virgin has filed an application with the National Arbitration Forum, a body which deals with domain name disputes.
The .xxx domains went on sale for the first time on 6 December.
Last week Icann, the body which has overall responsibility for the system, opened applications for afurther expansion of the net naming system.
Under the new scheme it will be possible to register almost any word as a domain name suffix.
Critics argued companies would have to spend large amounts of money to protect themselves from cybersquatters.
"We spend a lot of time protecting the Virgin brand and the Richard Branson name and increasingly this takes us online," a spokesman told the BBC.
"We do see this as a growing problem with the changes to top-level domains and we not alone," he added.
ICM Registry, which oversees the .xxx domains, had offered firms the chance to pay a one-off fee to protect their brands prior to the scheme's launch.
Virgin's claim will turn on factors such as whether the original registration was in good faith and what legitimate interest the present owner may have to the use of the name.