But rather than follow his family into the armed forces, the Hollywood star's play-acting led him to a very different career.
Yesterday, he was back at the Highland garrison, where both his father and grandfather served, to help launch a campaign to refurbish the Highlanders' Museum based there.
Grant, who starred in films including Four Weddings and a Funeral and About a Boy, said his own childhood was filled with happy memories about the base.
"As a child, I had holidays up here from the age of three," he said. "We were always playing about in the fort, playing at war on the battlements with my brother and girl cousins.
"I always found it all fascinating as there were so many soldiers in my family. I've got it in my genes, it's in my DNA.
"Weirdly, a military career never beckoned for me. I must be the first Grant to reach 17 or 18 without anyone saying 'how about the army?'."
Grant's grandfather, Colonel James Murray Grant, was the sixth generation of his family to serve as an officer. He joined the Seaforth Highlanders in 1918 and received the Distinguished Service Order for bravery and leadership at St Valery during the Second World War.
He went on to command the regimental depot at Fort George for many years after the war.
His son - Hugh Grant's father - Captain James Murray Grant, also had a military career. He was trained at Sandhurst and served with the Seaforth Highlanders for eight years in Malaya, Germany and Scotland.
During his visit yesterday to launch a public appeal to raise 3 million for the refurbishment project, Grant was shown a kilt, jacket and Balmoral bonnet worn by both his father and grandfather, as well as a memorial to the Grant Clan's association with the regiment. He said despite receiving hundreds of requests to help good causes, he had no hesitation in helping the museum appeal. "It feels personal. I wanted to do it for my father and grandfather. I feel a loyalty to the regiment; even though I was not a part of it myself, it feels like it's family.
"I have always been fascinated by the history of the Seaforths and other regiments. It's deep in my system and so anything I can do to raise the last bit of funds they need, then I'm delighted to help."
Grant said he also hoped Fort George could remain as a working garrison. It is presently home to the Black Watch but it has been rumoured the HQ may lose a military presence under defence cuts, although the museum would remain.