Stanley Metcalf, six, was found injured at a property in Sproatley, East Yorkshire, on July 26, last year.
His great-grandad, 78-year-old Albert Grannon today pleaded guilty to manslaughter by gross negligence and possession of a firearm without a certificate when he appeared at Hull Crown Court.
Stanley's family were in court to hear Grannon's plea.
He will be sentenced on July 2, at Sheffield Crown Court and was granted unconditional bail.
Judge Peter Kelson QC warned Grannon that he should prepare for a prison sentence.
Judge Kelson said: "It is important that I make clear to you that the mere fact I have ordered a pre-sentence report should not be taken by you as an indication to the likely sentence.
"This case whilst tragic is very serious and it is entirely possible that a prison sentence may follow and you must prepare for that."
Six-year-old Stanley was a huge fan of football and supported Hull City.
Football fans paid their own tribute to him when they had a minute of applause for him in the sixth minute of their match against Aston Villa in the first game of the Championship season last year.
Paying tribute to Stanley previously, his family 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.
"He was so vibrant and full of energy, a typical six-year-old boy who just wanted to have fun and enjoy life, and he adored playing football."
The statement added: "Stanley was a loving, caring and beautiful boy, and there is a huge gap in all our lives now that will just never be filled."