Prosecutor Sergeant Phil Berryman said the hunting party arrived on Stewart Island on March 22 and that evening discussed where they planned to hunt the next day.
Samuel Long said he was heading for a rata tree stand, about 550m from the hut where the group was staying.
The next morning Samuel Long left the hut about 9am dressed in camouflage gear.
Stephen Long left the hut about 9.45am.
The two men took a similar route for some time but Stephen Long intended to veer off before he reached the rata tree stand.
Stephen Long saw movement in the bush which he believed to be two white-tailed deer, Mr Berryman said. He took two to three minutes with his naked eye and his rifle scope to confirm it was deer, moving from left to right as he watched.
He saw what he thought was one deer move away, and the head of the remaining deer moving up and down as though the animal was feeding.
He believed he could see two [antler] prongs and believed the deer was a young white-tailed buck.
He fired one shot, but on walking to the clearing about 20m away found he had shot his son in the head, fatally injuring him.
Long told police his son should have been at the tree stand where he said he was going to be, Mr Berryman said.
He told police he was "convinced he was shooting a deer".
Long was remanded at large for sentencing on August 4.
Judge Cook did not enter a conviction and said the sentencing judge would consider submissions on whether Long should be discharged without conviction.
She ordered a pre-sentence report "to explore the options of home detention or community detention".
