Kirk, 101, appeared on grandson Cameron Douglas' Instagram as he looked lovingly at baby Lua Izzy.
Cameron, whose dad is Kirk's son Michael Douglas, posted the black and white photo on Instagram and wrote alongside it: "LOVE."
Lua Izzy can be seen in a cute white dress in the shot as she reaches out to her great-granddad.
While Kirk, who is best known for the 1960 film Spartacus, is wearing a tracksuit teamed with slippers and a pair of sunglasses.
Cameron, 39, and his partner, Viviane Thibes, welcomed their daughter last December.
He told PEOPLE at the time: "Since Viviane has given birth to a beautiful healthy girl on Monday afternoon, I’ve been at their side ever since. I’m very happy.”
Lua Izzy’s middle name is a tribute to Kirk, who was born Issur Danielovitch and later went by Izzy.
Cameron's dad Michael recently opened up about his son's struggle with drugs, calling it a "nightmare."
He said: "My son's struggle was a nightmare.
"It was stressful for all involved, very painful and difficult. I'm happy to say he's in wonderful shape now."
Michael, 73, added: "He's been out of federal prison for a year and a half and he's actively pursuing his career."
Cameron Douglas served almost seven years in prison for drug charges, and was released in August 2016.
His five-year sentence for possession of heroin and selling methamphetamine was extended after he admitted to smuggling drugs into prison.
Speaking about how Cameron is as a father, Michael told Entertainment Tonight: "Lua is the most beautiful little girl.
"I couldn't be more happy, and it's just great to see him be such a great father."
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