The Scandinavian country received 36,207 asylum applications last year, up from 24,300 in 2006, the Swedish Migration Board said in a statement.
The number of Iraqis seeking shelter in Sweden more than doubled, from 8,951 in 2006 to 18,559 a year later.
The figures for Somali applicants more than tripled, from 1,066 in 2006 to 3,349 in 2007.
More children applied for asylum on their own last year, said the immigration authority.
Minors from war-ravaged Iraq, Somalia and Afghanistan accounted for most of the 1,264 applications in this category.
The Migration Board said it had granted half of all applications last year, up from 40 percent in 2006.
Explaining the increase, Swedish Migration Minister Tobias Billström told the TT news agency: “Many people have obviously cited reasons that we think give them a right to shelter.”