The 26-year-old said the video of the three-time surfing world champion being attacked in South Africa on Sunday had brought back memories of his own experience.
"He looked pretty shaken up, and I remember that's how I felt after it had happened."
Fanning told media in Sydney yesterday that he was keen to return to the water despite his close call.
Dr Grant said it was the same for him after his attack.
"It hasn't set me back at all, I was out most days over the summer diving for crayfish in the shark infested waters around Ruapuke Island in Foveaux Strait.
"There was one day I went for a dive after seeing [a] shark fin pass by the boat but it didn't cause us any bother and I didn't even see it when I was in the water."
He said when you are out spearfishing that was one of the risks you took, and he has accepted that.
Dr Grant said the video of Fanning's attack had also reignited the topic with his friends and family.
"It's funny talking about it at work with people, they are just bringing up that story again.
"But we all thought the funnier part of the story was the media response to it - at the time it was more of just something that happened at the weekend, we didn't care that much about it, but then the media picked up on the story and it went all around the world."