The Ipsos MORI survey indicated fewer than one in 20 people supported deer hunting remaining legal, fewer than one in eight supported hare hunting remaining legal and fewer than one in five supported fox hunting remaining legal.
Mr Oddie said Northern Ireland remained the last place in the UK where such dog hunting was permitted.
Ahead of a visit to Stormont, he said: “The people of Northern Ireland have spoken: they want hunting with dogs banned in their beautiful part of the world.
“Cruelty to wild animals in the name of sport has no place anywhere in the 21st century”.
Janice Watts, from League Against Cruel Sports NI, added: “It’s clear from our MORI survey that most people in Northern Ireland view hunting with disgust. Three out of five people actually think this cruel activity is already illegal so it’s high time our representatives brought in a law to ban hunting.
“Our new charter urging members of the Northern Ireland Assembly to introduce new anti-hunting legislation is endorsed by animal welfare organisations across the country, reflecting the strength of feeling for a complete ban.”