Internet ads accounted for a third as many complaints as television ads and half as many complaints as national press ads, the ASA said.
Last year 2,066 complaints were made to self-regulatory body the ASA about internet adverts; in 2005 that figure was 1,577.
"Second most complained about [non-broadcast medium] was the internet, with 2,066 complaints, representing a 32.7% year-on-year rise," said the ASA's annual report. "Five years ago, in 2001, the internet ranked as the eighth most complained about of all non-broadcast media."
The most common reason for complaints about non-broadcast media adverts was that they were misleading.
While the number of internet-related complaints spiked, the number of complaints relating to email dropped by more than 10%. The 276 complaints received last year was a reduction from the 313 received in 2005.
There were 41 complaints about adverts transmitted via text messages, fewer than half the number of SMS-related complaints received in 2005. Three complaints related to voicemail adverts, compared to five in the previous year.
Reflecting the growing trend for computer game developers to earn extra revenue by allowing advertising in their virtual worlds, one complaint last year related to an advert in a computer game.
There was an almost tenfold increase in the number of complaints relating to 'electronic' media. That category attracted 19 complaints in 2005 and 188 in 2006.
