Speaking to Journalism.co.uk, Grimshaw said he was confident that people would pay for 24-hour access to FT.com.
"It's reasonable to assume there are a lot of people who will quite happily pay that, but aren't willing to commit to one year's subscription in one go," Grimshaw said.
Grimshaw added that the FT would like to consider introducing micropayments, but said the technology did not yet exist.
This could change later this year with reports that Apple plans to introduce a web version of its iTunes service that would allow publishers to charge on a per article basis.
New mobile versions of the FT's mobile app are also on the way. More than 200,000 of these have already been downloaded and a new Blackberry and Android version is planned.
Changes to the FT's charging model, which currently costs between £171 (US$ 276) standard and £259 (US$ 418) premium a year, comes as pay wall activity on both sides of the Atlantic heightens.
The New York Times last week announced it would move ahead with a metered paid content model in 2011 and News International has appointed a new boss to oversee The Times in London's move to a pay wall expected to launch in the spring.
Gurtej Sandhu, senior-vice president of new media at Rupert Murdoch's Star TV, has been appointed as director of Times Digital.
Working out of India and Hong Kong, Sandhu established the digital division for News Corporation's Star TV. He was previously based in the UK and worked at News International and United Business Media.