Raymond William Twiddle came under investigation after a member of the public reported seeing a man killing gosling chicks with a spade and then burying them.
Officers with specialist wildlife crime expertise attended the scene in West Knapton, near Malton, after the report was received on April 24.
They found two greylag gosling chicks buried in a disturbed mole hill and a third in long grass.
Post mortem examinations by a vet confirmed blunt trauma as the cause of death.
Greylag geese are protected by the Wildlife and Countryside Act 1981 and are amber listed due to conservation concern in the UK.
Twiddle, 83, of West Knapton, pleaded guilty during a hearing at Scarborough Magistrates Court on Monday.
He was fined Â£8,100 and ordered to pay a victim surcharge of Â£170 and Â£85 prosecution costs.
Wildlife crime officer PC Graham Bilton said: "The actions of the person involved not only resulted in the death of the young goslings but also caused a great deal of stress to the parent birds, who were still present when we arrived.
"The public need to be aware that anyone committing rural and wildlife crime will be robustly dealt with, and the incident again highlights the essential and continual hard work of wildlife crime officers."
North Yorkshire Police worked closely with the RSPCA, RSPB and Crown Prosecution Service to secure a conviction in this case.
Sally Robinson, from the CPS, said: "This was a sickening and barbaric act. We were able to work with our partner agencies to build a robust case to put before the court.
"The severity of the penalty imposed in this case is a clear indication that such acts of wilful cruelty will be punished with the full force of the law."