The survey, carried out by researchers Sifo and the Aftonbladet newspaper, showed that 70 percent of Swedes were happy to keep the monarchy, however a majority of respondents wanted to see a change.
When asked if they wanted to see the king abdicate to make way for Crown Princess Victoria, 23 percent said "Yes, within ten years", 20 percent responded "Yes, within five years" and 17 percent said "Yes, as soon as possible".
"This is a truly high figure," said project leader Jon Andersson of Sifo to the Aftonbladet newspaper.
"It's really six in ten Swedes who want the king to leave his post early."
The king, who will celebrate 40 years on the throne in mid-September, suffered intense media scrutiny after his rumoured infidelities were detailed in a tell-all biography published in late 2010.
17 percent of people responded that their confidence in the king has dropped in the past year, while 79 percent claimed their level of trust has not changed.
"Even if the confidence in the king is lower, the trust in the monarchy is relatively stable and has been for a long time," explained statistician Henrik Oscarsson of the Gothenburg University to the paper.
The survey was carried out between the 10th and 13th of December, and 1,000 people were interviewed.