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The court's seven justices will spend an hour hearing arguments on the appeal and then will have three months to issue a written ruling.
Klaas' father, Marc Klaas says he does not expect Davis will ever be executed.
"I have no expectation that Richard Allen Davis will ever be executed, I suspect he will die of whatever miserable affliction he dies of and can only hope it's as painful as humanly possible," Klaas said.
Davis, 54, a former sheet metal worker with a long criminal record, was convicted in Santa Clara County Superior Court in 1996 of kidnapping the girl from a slumber party at her mother's home in Petaluma on Oct. 1, 1993, and murdering her by strangling her.
Her body was found near U.S. Highway 101 in the Cloverdale area two months after the kidnapping after Davis, who had been arrested for a parole violation, gave investigators information about the location.
The trial was moved from Sonoma County to Santa Clara County because of extensive publicity about the case.
All death penalty cases in California are automatically appealed directly to the state Supreme Court.
The direct appeal is the first step in a lengthy appeal process. If the state high court upholds his conviction, Davis can continue appeals through habeas corpus petitions in the state and federal court systems.
Davis' case led to California's voter-approved "three strikes" law, which provides lengthy sentences for repeat offenders.
ABC7 News contributed to this story.
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