The US-based church argues that the book is reserved for key members of the religion and should be kept secret.
It says international copyright laws should stop the unpublished material from falling into the public domain.
But after the court ruling last week, Swedes are now free to go to places where the document is kept, such as the Swedish parliament, and read the material.
However, the church plans to fight the decision. It has launched a campaign that involves its members borrowing the book constantly, thus making it virtually impossible for anyone else to see it.
Tarja Vulto, a church spokeswoman, said only 300 to 350 of the religion's 8 million members had rightful access to the book.