A 4.5 metre crocodile that had been stalking in waters close to the small community of Palumpa in the Daly River Reserve of the Northern Territory has been captured and shot.

Locals say the crocodile is the one that had been a problem for about two years in the area.

They say the big saltie sometimes stopped children from crossing the causeway at the community to attend school.

Senior wildlife ranger Tommy Nichols says police and council officers trapped and shot the large crocodile in a billabong on the outskirts of Palumpa, about 240 kilometres south-west of Darwin.

"We had a report the other day that there was a large crocodile there that was menacing the kids," he said.

It's the second four-metre-plus crocodile captured in the Territory in a week.

Another was harpooned near Borroloola in the Gulf Country after reports that it had attacked a horse.