The camera footage shows a goshawk - a protected species - caught in a trap on Howdale Moor, near Goathland in the North York Moors, in the early hours of May 2.
Soon after the bird is trapped, a man with their face obscured is seen deliberately killing the raptor and removing its body in a bag.
The crime took place within the National Park boundary. The North York Moors are one of the UK's black spots for raptor persecution. The area is home to a large number of commercial grouse moors, and birds of prey feed on game birds.
The grouse shooting season begins on August 12.
Peregrine falcons, hen harriers, buzzards and goshawks are often targeted for persecution associated with shoots. In some areas, they have become locally extinct or critically endangered.
North Yorkshire Police wildlife crime officer Jeremy Walmsley said: ”The goshawk is one of the most protected species of bird in the UK and it is extremely distressing that an individual would choose to kill any bird of prey. I appeal to anyone with information about this horrific crime to get in touch with the police and help us to find the person responsible for the death of this magnificent bird.
“We see far too many incidents of birds of prey killed or injured in North Yorkshire and as a police force we are doing all we can to put a stop to this inhumane and callous crime.”
Goshawks were persecuted to the extent that they became extinct in the UK in the late nineteenth century, and numbers have only slowly recovered since then.
A cage trap can be used legally to catch certain species of birds and is designed to contain them humanely, in case of any non-target species becoming caught. Non-verminous birds with protected status should be released immediately if accidentally trapped.
Killing a bird of prey is an offence under the Wildlife and Countryside Act 1981.
If you have any information which could help this investigation, please call 101 quoting reference: 12200073462 or if you wish to remain anonymous contact Crimestoppers on 0800 555 111.