Earnest Dykes, 36, was convicted and sentenced to death in Alameda County Superior Court in 1995 for the first-degree murder of 9-year-old Lance Clark on July 26, 1993.
Dykes was also convicted of the attempted murder of the boy's 70-year-old grandmother, Bernice Clark, who owned the Oakland apartment building where Dykes lived with his mother.
Dykes, who was 20 at the time, shot the victims in Bernice Clark's car in the apartment building parking lot while attempting to steal her wallet.
The high court, in a ruling issued in San Francisco, unanimously rejected a series of appeal arguments, included Dykes' claim that a confession he gave police should not have been admitted as evidence. Dykes had given up his right to have a lawyer present before making the confession.
The court said "there is no indication of police coercion" before or during the confession.
Dykes contended in the statement to police and in testimony at his trial that the shootings were an accident during the robbery.
Dykes' lawyer in the appeal, Karen Landau, said Dykes will continue appeals through habeas corpus petitions in state and federal courts.