Iceland was the runner-up taking second place and Azerbaijan claimed third position.
British singer Jade Ewen, who was singing an Andrew Lloyd Webber number, came fifth, which was a lot better than last year when the UK were at the bottom of the list.
Voting in the Eurovision Song Contest final was divided between televoting and panels of musical experts, and a total of 42 countries voted for their choice from the 25 songs in the competition.
Alexander Rybak, who was born in Russia and is is also a classical pianist, is a famous musician in Norway and he wrote his country's winning entry, Fairytale.
In the past the highest score had been awarded to Finland's Lordi with Hard Rock Hallelujah in 2006 but Norway has now beaten their fellow Scandinavian neighbour.
