An Alabama man convicted of murdering a female hitchhiker in 1994 became the third person in US history to be executed by nitrogen gas.

Carey Dale Grayson, 50, was convicted of capital murder in 1996 and was executed on Thursday for the death of then 37-year-old Vickie Deblieux.

His lawyers argued for the US Supreme Court to review the constitutionality of the new execution method, but the high court halted a petition that would have stopped the execution.

No other state has used nitrogen hypoxia to carry out the death sentence.

Grayson was executed at the William C. Holman Correction Facility in Alabama for the murder, and members of his victim's family protested the act.

Jodi Haley, Deblieux's daughter who was 12 at the time of the murder, told reporters after the execution that Grayson was abused in his youth. She said that "society failed this man as a child, and my family suffered because of it".

"Murdering inmates under the guise of justice needs to stop," she said. She added that "no one should have the right to take a person's possibilities, days, and life".

Alabama began using nitrogen gas this year to carry out death sentences. It involves using a respirator gas mask to replace breathable air with pure nitrogen gas that results in a lack of oxygen.

Grayson's attorneys argued the new method causes "conscious suffocation" and does not result in swift unconsciousness.

But state attorneys pointed to two prior executions of prisoners who died by nitrogen hypoxia earlier this year. The latest took place last month.

Grayson made obscene gestures before the execution on Thursday and shook while taking gasping breaths when the gas began flowing, US media reports.

He was one of four teenagers convicted in the killing of Deblieux and the only one who was over the age of 18 at the time of the murder. He was the only one to receive the death sentence.

Deblieux was planning to hitchhike from Tennessee to Louisiana when she was picked up by the four teenagers in Alabama.

The teenagers took her to a wooded area where they beat her, stood on her throat and threw her body off a cliff.

They later returned to the mountain where they mutilated her body by stabbing and cutting her 180 times and removing parts of her fingers.

Deblieux's body was later found by three rock climbers. A medical examiner said every bone in her face was fractured at least once.

"My prayer for Vickie’s family is that they can find solace in the state of Alabama finally serving justice for their heart-breaking loss," Alabama Attorney General Steve Marshall said in a statement. "And my hope is that one day it will not take three decades to provide justice for other victims of violent crimes."