This undated photo shows the San Quentin Prison execution chamber in 2005. Picture: The California Department of Corrections

Huntsville, Texas - A Houston man facing execution for killing his 15-year-old girlfriend, her mother and her grandfather 13 years ago is looking to the US Supreme Court to stop his lethal injection.

Derrick Dewayne Charles is set to die Tuesday evening.

The 32-year-old would be the seventh prisoner executed this year in Texas, the nation’s most active capital punishment state.

His attorneys are arguing that he’s mentally incompetent for execution and that they need time and court-approved money for experts and investigators to pursue that claim.

State attorneys say questions about his competency were rejected in earlier rounds of appeals and there’s no evidence he’s incompetent.

Charles in 2003 pleaded guilty to capital murder charges.

He was on parole for a burglary conviction at the time of the triple slaying.