Point One Marketing - trading as Stop the Calls - was said to have operated in a "bullying and aggressive way".
The company, based in Bournemouth, claimed it was an official service to stop nuisance calls.
It was fined Â£50,000 by the Information Commissioner's Office (ICO), following hundreds of complaints.
Some people said they had been shouted at when they asked the company not to call them again.
One woman who suffered from dementia was persuaded to hand over her credit card details.
"They tried to sell a product that they claimed would stop nuisance calls, knowing full well they were responsible for so many such calls themselves," said the ICO's head of enforcement, Stephen Eckersley.
"That they operated in what appears to have been such a bullying, aggressive way only makes matters worse."
The official way to stop nuisance calls is through the Telephone Preference Service, which is free to use.
A firm that promised to block all nuisance calls has been fined by the Information Commissioner - for making nuisance calls itself.