Ronnie Zape, the 39-year-old duty officer of the Bow Eagle, has been charged with failing to attempt to save the fishing boats crew and faces a maximum sentence of six years in prison in Norway.
The verdict is expected on Thursday.
Zape was in command when the 170-meter Bow Eagle crashed into the 26-meter Cistude off Frances Atlantic coast, killing four of the seven fishermen on board.
While the Bow Eagle steamed away from the scene without initiating any rescue procedures, the three survivors spent more than eight hours in the water before being rescued.
Zape and a young Filipino sailor who was also on the bridge at the time of the accident initially kept silent about the collision because, they initially argued, they thought they had only grazed the Cistude.
But the sailor, filled with remorse, defied Zapes orders to keep mum and told the truth to the second-in-command, who later informed authorities of the ships involvement in the accident.
Zape is being tried in Norway because the accident occurred in international waters and the Bow Eagle is a Norwegian-flagged ship, owned by the Odfjell shipping group.
According to the conclusions of a French maritime inquiry published in October, the Cistudes night watch crew was not vigilant enough at the time of the accident.
The trawler, which did not have the right of way, did not make any attempt to get out of the tankers way, experts said.
However they stressed the Bow Eagle crews "inadequate behaviour" in failing to help the fishermen.