The pro file-sharing Pirate Party still look like getting a seat in the next European Parliament, while the far-right Sweden Democrats look like missing out.
The poll, which was carried out by polling institute SIFO for the broadsheet Svenska Dagbladet, revealed the following figures:
Social Democrats: 31.7 procent (-0.2% compared to the last poll)
Conservative Moderates: 22.6% (-1.3%)
Green Party 10.2% (+1.0%)
Liberals: 10.1 (+0.8)
Left Party: 6.5 (+1.4)
Pirate Party: 6.0 (+0.1)
Centre Party 5.2 (-0.3)
Christian Democrats: 3.1 (-0.5)
Sweden Democrats: 2.3 (+0.2)
June List: 1.9 (+0.1)
SIFO asked 1896 Swedes how they would vote in the upcoming EU election between 18th and 28th June.
Parties have to gain 4% of the national vote to win a seat in the European Parliament, according to the Swedish system of proportional representation. Sweden's current centre-right government is made up of the conservative Moderate, Liberal, Centre and Christian Democrat parties.
Polling stations are already open in Sweden for early and postal voting, the official election day is next Sunday.
You can find out more about the various political parties and their election manifestos by visiting our .