Only 15.4 percent are in favour of searching for oil while the rest declined to answer, according to the survey of 2,772 people carried out in early November by the regional government of the islands which is opposed to oil prospecting.
Spanish oil giant Repsol began drilling for oil on November 18 some 50 kilometres (30 miles) from the islands of Lanzarote and Fuerteventura, off the west coast of Africa.
Spain's Industry Ministry in August authorized the company to search for oil in the region at three locations at depths ranging from three to seven kilometres despite fierce opposition from environmentalists and local residents.
Fearing a loss to the tourism industry, the government had called a referendum for November 23rd to ask residents of the archipelago, which is home to just over two million people, if they backed oil prospecting, but the national government blocked the ballot in the courts.
The head of the regional government of the Canary Islands, Paulino Rivero, has accused the central government of showing preferential treatment to the Balearic Islands, a region run by the ruling Popular Party and which is also the target of an oil exploration project.
Prime Minister Mariano Rajoy has said his government would not allow oil exploration off the Balearic Islands if it presented the slightest environmental risk.
Spain imports nearly 80 percent of its energy and the central government argues it can no longer afford the luxury of holding back business or wasting natural resources.
But locals and green groups fear Repsol's prospecting will harm local flora and fauna such as dolphins and disrupt the tourism industry that is vital to the area's economy.
The Spanish government last week impounded a Greenpeace campaign ship, the Arctic sunrise, which entered a restricted zone to protest against the search for oil.
The Canary Islands are Spain's third most popular destination after Catalonia and the Balearic Islands.
The archipelago received 10.6 million foreign visitors last year, 17.5 percent of the total number of visitors to Spain.