Pollsters Sifo, on behalf of magazine Svensk Damtidning, asked almost 1,200 people who their favourite members of the royal family were.
Almost one in two picked Crown Princess Victoria, the heir to the throne, while only two out of ten chose her father the King.
King Carl XVI Gustaf, who turned 70 last year, has been on the throne for 43 years. Forty percent of respondents told the survey they thought he should follow in the footsteps of the Queen of the Netherlands, Beatrix, who abdicated four years ago in favour of her eldest son Willem-Alexander.
Eleven percent said he should do so within a year, while 29 percent said within five to ten years.
However, 38 percent said Victoria should not take over the throne until he passes away.
Victoria, who turns 40 this summer, married Prince Daniel, her former personal trainer, in 2010. They have two children and live at Haga Palace in the Haga Park north of Stockholm.
The survey also asked if people thought Princess Madeleine, who currently lives in London with her husband Chris O'Neill and their two children, should move back to Sweden. Two out of ten said “yes”, three out of ten “no” and half “don't know”.