Simpson's lawyers turned in their 20,000-word appeal last month but were told by the court to reformat it.
The new 102-page document filed Wednesday asks the high court to reconsider whether Simpson's trial attorney in 2008 had conflicts of interest and botched his defence.
Simpson's former attorney, Yale Galanter, notes that a Nevada judge ruled last year that Simpson failed to demonstrate how Galanter's actions changed the outcome of the case.
That judge said evidence was overwhelming that Simpson orchestrated the September 2007 kidnapping and robbery of two sports memorabilia dealers.
Next week is the 20th anniversary of the slaying of Simpson's ex-wife and another man in Los Angeles.