The Four Weddings and a Funeral star was one of the leading celebrity campaigners against press intrusion after Murdoch's now defunct British tabloid the News of the World was hit by allegations a private investigator intercepted voicemails for the publication.
A number of stars including Jude Law, Sadie Frost and Charlotte Church have been awarded damages from Murdoch's news company, and now Grant has filed his own claim at London's High Court - 24 hours before the Friday (14Sep12) deadline.
Another 100 claimants seeking damages are expected to be received before the cut-off point, which was set by the judge presiding over the civil cases.
Last November (11), Grant made a headline-grabbing appearance at The Leveson Inquiry, an investigation into press ethics which was prompted by the furore over the hacking accusations.
He claimed his privacy had regularly been invaded by tabloid newspapers and he had been "chased at speed" by photographers.