Albert Grannon, 78, pleaded guilty yesterday to the manslaughter of Stanley Metcalf at a house in Sproatley, East Yorkshire, last year.
Six-year-old Stanley suffered a hole in the side of his abdomen when he was shot with an air rifle on July 26.
Grannon, who also admitted possessing an air rifle without holding a firearms certificate, sat in the dock at Hull Crown Court wearing a checked jacket, shirt and tie, and listened to the brief proceedings through a headset.
John Elvidge QC, prosecuting, adjourned the hearing for pre-sentence reports to be carried out and the case was transferred to Sheffield.
Family members were seated in the public gallery and on chairs within the courtroom normally reserved for jury members yesterday.
No details around the circumstances surrounding the offence were given.
In a statement issued following Stanley's death, his family described him as ‘vibrant and full of energy’.
They said: "We are absolutely devastated and completely heartbroken without Stanley and it still doesn't feel real we won't see his happy, smiling face again.
"There are no real words to express how the loss of Stanley has affected us and we all miss him so much.
"Stanley was a loving, caring and beautiful boy."
His great-grandfather, Grannon, has been granted conditional bail ahead of the sentencing date.
He was warned that prison is a possibility.
Judge Peter Kelson QC told the defendant: "It is important I make clear to you the mere fact I am ordering a pre-sentence report and renewing your bail should not be taken by you as any indication as to the likely sentence.
"This case, while tragic, is very serious and it's entirely possible that a prison sentence will follow and you must prepare for that."
Detective Inspector Rebecca Dickinson, who led the investigation for Humberside Police, said she was pleased that Grannon - who she said had shown no remorse until this point - had ‘faced up to the enormity of his actions’.
She said: "This was an extremely tragic incident where a six-year-old boy who had all his life ahead of him had it cut so needlessly short.
"It makes it all the more tragic that it was a member of his own family who was ultimately responsible for his untimely death."
The detective added: "It is a nightmare that Stanley's family have had to live through every day since last July, and will have to live through from now on."
Describing the effect of Stanley's death on his ‘inseparable’ twin, Elsie, she added: "I can only imagine what she will feel like now and when she reaches any milestones in her life, knowing that she should be sharing them with Stanley.
"There are no winners in this at all."