The survey, carried out by Ipsos MMI, found that a full 62 percent of Norwegians who said they were worried about a war or attack on Norwegian soil, up from 45 percent in 2014.
The percentage who described themselves as "quite" or "very" worried was up from 13 percent to 22 percent.
Women, young people and residents of Finnmark a county close to the Russian border, were the most concerned.
Norway's chief of defence Haakon Bruun-Hanssen played down the possibility that Norway or another NATO country might be invaded in the near future.
”Increasingly tense relations with Russia, the use of military force in Ukraine, and an increased threat from terrorist organisations such as IS make people more aware of a possible threat,” he told Norway's Aftenposten newspaper. ”With the background information I have, I don't share the same concern. But with the focus of the media in recent years, I understand why people are concerned.
The survey also revealed that Norwegians have less confident in the ability of their armed forces to protect them, with one in four agreeing that the army is poorly or very poorly equipped for protecting Norwegian borders.
The trend was especially strong in Finnmark, close to the Russian border, where only 24 percent said they were confident in the armed forces' ability to protect borders, compared to 44 percent in 2014.
The survey, released on Friday, comes at the same time as claims that Russian troops have been rehearsing an invasion of northern Norway, and the islands of Åland, Gotland and Bornholm.