North Yorkshire Police are continuing to investigate the circumstances surrounding the killing of the bird of prey, which was found dead near Malham last week.
The discovery came just a few days after another buzzard had been found with cuts to its head and both feet at Norton, near Malton.
Park authority chairman Carl Lis today condemned the attacks on wildlife.
“The shooting of this buzzard was a mindless and barbaric act," he said.
"The fact that it only extends a long list of recent incidents makes it no less upsetting. I urge anyone who may have information to contact police.”
Police previously said a farmer had found the dead bird's body in a field close to Gordale on 16 May.
Further examinations are ongoing after the bird was taken to Abbey House vets in Leeds, where an X-ray revealed a shotgun pellet lodged in its head.
Mr Lis said: "The person who shot this bird needs to know that their criminality risks hitting local businesses in the pocket.
"Birds of prey are a big attraction to visitors that come each year to the National Park. This buzzard was shot a short distance from Malham Cove, where nesting peregrines attract thousands of tourists.”
The buzzard found in Northton was still alive and an x-ray examination showed that the bird had been shot too, this time in the leg.
After receiving treatment at a local specialist centre, it was released back into the wild yesterday.
The RSPB said the illegal shooting of birds of prey was an ongoing problem in North Yorkshire, with red kites and other birds also being targeted.
This is despite the penalty of a fine and up to six months in jail for anyone caught doing so.
Jenny Shelton, RSPB investigations liaison officer, said: “It is alarming to hear of yet another bird of prey being shot down in North Yorkshire.
"The sight of a buzzard soaring high overhead is one of the joys of the British summer and no-one should take that away from us.
"Sadly, North Yorkshire is proving the worst county in England for these sorts of crimes. It is a serious, ongoing problem and it has to stop.”
Anyone with information on the incident near Malham is asked call North Yorkshire police on 101, quoting reference 12170089221.
If you find a wild bird which you suspect has been illegally killed, contact police and RSPB investigations on 01767 680551 or fill in the online form on the charity's website.