But animal rights group PETA has protested the move, saying that witnessing the sport could "damage a child's psyche" and "desensitise George to the suffering of animals".
PETA director Mimi Bekhechi said few people in 2020 viewed shooting for sport as "anything other than a violent perversion".
"For a child to be compelled to witness such casual killing – and by a parent he looks up to, no less – is potentially as harmful to his or her psyche as it is to the bird's very life.
"It can desensitise children to the suffering of animals – which is cause for concern, given the well-established link between cruelty to animals in childhood and antisocial behaviour in adulthood – and could give George nightmares.
"To help him grow into a responsible, compassionate leader, his parents must teach him respect for all living beings."
Both William and Harry have hunted from a young age, and were so enthusiastic that their mum Diana jokingly called them her "Killer Whales".
Hunting and shooting is a traditional activity in the royal family. Photo / Getty Images
But Harry has hunted much less frequently since meeting Meghan, as the duchess is known not to approve.
It's believed that Kate accompanied William and George on Saturday, leaving Charlotte, 5, and Louis, 2, at their lodgings. Kensington Palace declined to comment.
The Royal Family has a long history of the sport, though the Queen has made an effort in recent years to prevent them being photographed while taking part.
It's an especially fine line for Prince William, who balances his passion for hunting with his work on high-profile conservation campaigns.
He faced heavy criticism in 2014 for going on a boar hunting trip with Harry on the Duke of Westminster's Spanish estate just days ahead of joining a campaign against poaching and the illegal wildlife trade.
However, none of the animals they killed were protected species. And Kensington Palace officials have always defended William, saying that legal private shooting and hunting is very different from the illegal wildlife trade he is taking steps to combat.
William's United For Wildlife campaign has been praised for its work to protect endangered species like rhinos, tigers, elephants and pangolins.
Even Kate has been snapped with a gun in her hands over the years shooting grouse and pheasants, while she and her parents Michael and Carole Middleton have learned to stalk deer on the Queen's Scottish estate.
