Kourtney, Kim, Khloe and Robert Kardashian, along with their mother, Kris Jenner, filed the complaint in a Los Angeles federal court this week.
The family alleges the late lawyer Robert Kardashian's third wife, Ellen Pearson, has no right to possess or profit from the articles, since she and Robert were only married for two months before he died of esophageal cancer in 2003.
The family is seeking at least $500,000 in damages, claiming Pearson had no right to sell photos and excerpts from the journal to the media against their wishes.
The Kardashian family patriarch was best known as part of the so-called dream team of defense lawyers who helped win an acquittal for former football star O.J. Simpson at his murder trial.
Robert Kardashian's children and ex-wife later earned fame for building a reality television empire.