Privacy campaigners are seeking to stop GCHQ using "unlawful hacking" to help its surveillance efforts.
Privacy International said the UK intelligence service has infected millions of devices to spy on citizens and scoop up personal data.
A 30-page legal complaint has been filed with the Investigatory Powers Tribunal which monitors whether the UK's spying laws are being observed.
GCHQ said it had no comment to make on the legal complaint.
In a statement, the Privacy International pressure group said the documents released by Edward Snowden had detailed the many ways that GCHQ was spying on people, many of which violated the European Convention on Human Rights which guarantees a right to privacy and to freedom of expression.
GCHQ and NSA programmes uncovered by Mr Snowden let the agencies listen via microphones, watch through webcams and scoop up detailed web browsing histories, said Privacy International.
Eric King, deputy director of Privacy International, said the surveillance was the modern equivalent of the government entering someone's house and reading their diary, correspondence and journals.
The freedom GCHQ and the NSA had to carry out surveillance was equivalent to "covert, complete, real-time physical and electronic surveillance", he said.
"Arbitrary powers such as these are the purview of dictatorships not democracies," he said. "Unrestrained, unregulated government spying of this kind is the antithesis of the rule of law and government must be held accountable for their actions."
The IPT has yet to respond to the filing of the complaint.
Prof Richard Aldrich, a lecturer at the University of Warwick who has written a history of GCHQ, said the agency was much more worried about such legal challenges than ever before as judges had become "much more unpredictable in this area" than they were a decade ago.
The legal challenge comes only days after the Home Affairs select committee said oversight of the intelligence agencies was "weak".