A gunman who shot a cow in its rear on a West Coast farm, leaving it for dead, will have their firearms licence revoked if police catch them.

Greymouth police Senior Constable Mike Tinnelly said today that the animal was shot some time on Tuesday night and a vet had to be called out to put it down.

"What these people have done is complete stupidity and they should not even have a firearms licence if they cannot identify their target correctly."

Mr Tinnelly said the 550kg red and white hereford would have been easily recognisable as it was in a paddock close to the road.

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"Anyone who has information about the shooting should contact the police and we will take those responsible to court as well as taking their licence off them."

Mr Tinnelly said that the shooting took place close to a farmhouse on Blairs Road, which was not safe.

"Even if shooting the cow was a mistake, people who do not identify their targets do not deserve to have a firearms licence and they should have informed the farmer."

Mr Tinnelly said police would be increasing patrols of country areas in an attempt to catch the culprits.

The incident was costly for the farmer as the animal was worth about $2000, before the vet bills.