While 46 percent think there is the right amount of immigrants, or that Sweden should let in more.
This compares to a figure of 55 percent opposing immigration ten years ago, but is up from 37 percent last year.
Polling company Sifo asked a random selection of people to join a web-panel. Fewer than half accepted, but this still left 1,001.
Of those that responded 16 percent say that the Sweden Democrats have the best policy on immigration. This is three times as many as voted for the party in the 2010 election and still double what the party has recently been polling.
But almost half (47 percent) of those asked do not know which party is “best” on the immigration question. The head of analysis at Sifo says this may mean many simply do not see it as an important issue.