It was originally thought that Mark Bridger's appeal bid would be heard by leading judges at the Court of Appeal in London on January 24.
Bridger, a father of six, snatched April near her home in Machynlleth, Mid Wales, on 1st October 2012. Her body has never been found.
Sentencing Bridger in May, Mr Justice Griffith Williams said: "There is no doubt in my mind that you are a paedophile, who has for some time harboured sexual and morbid fantasies about young girls."
The move by Mark Bridger to abandon his application for appeal against his whole-life sentence was confirmed today by the Judicial Office.
Bridger kidnapped the child before sexually abusing her, murdering her and disposing of her body.
The former slaughterhouse worker was given the whole-life sentence by trial judge Mr Justice Griffith Williams after he was convicted by a jury at Mold Crown Court.
Mark Bridger, who was convicted of the murder of five-year-old April Jones, has abandoned his application for permission to appeal against his whole-life tariff, the Judicial Office confirmed today.
The mother of murdered schoolgirl April Jones has said her family continues to be "tortured" by Mark Bridger.
Bridger, who was convicted for the five-year-old's murder, has launched a legal appeal.
Coral Jones said she continues to be "tortured" by Bridger, jailed for life in May.
She claimed that Bridger had tried to claim compensation following an attack by a fellow inmate while at the top security Wakefield Prison, West Yorkshire, earlier this year.
"It's disgusting. He's in prison where he belongs and he should stay there," Mrs Jones told The Sun.
"He's just torturing my family with these legal battles. It's like he's taunting us, like he wants to show he's got the upper hand."
Murderer Mark Bridger, who was jailed for killing five-year-old April Jones, has launched a legal bid, the girl's parents told The Sun.
Parents Coral and Paul Jones said police warned them of an initial hearing at the Court of Appeal next month, which the couple plan to attend.
It is not known whether the appeal is against his conviction or sentence.
Bridger, a father of six, snatched April near her home in Machynlleth, Wales, on October 1 last year.
The five-year-old's body has never been found.
Prosecutor Jonathan Sharp said: "The defendant saw him and walked directly up to him with the blade held between thumb and forefinger.
"He then slashed him down the face, causing a deep wound extending from temple to chin.
"He paused for a moment and looked Bridger directly in the eyes, in Bridger's own words 'as if to admire his work or show me who it was'."
The child killer also suffered a cut to his arm as he tried to defend himself.
Bridger needed more than 30 stitches to the face wound, which required surgery under general anaesthetic. He will be scarred for life.
Ferreira and other life prisoners had talked about attacking Bridger to make him reveal the whereabouts of April's body, police were told.
The premeditated attack happened three days after Bridger was allowed to associate with other prisoners.
Ferreira made a weapon out of a prison-issue razor with extra blades attached to the handle.
A life prisoner slashed child killer Mark Bridger from temple to chin, severing an artery, in an attempt to get him to reveal where April Jones's body was hidden, a court was told.
Convicted murderer and rapist Juvinal Ferreira attacked Bridger with a knife made from a razor at top security Wakefield Prison in July.
He was sentenced to a second life sentence at Leeds Crown Court and had five years added to his minimum term, meaning he will not be released before 2036.
The devastated parents of murdered April Jones are finally able to plan a funeral for their daughter - almost 12 months after the schoolgirl was murdered. April, five, was snatched by Mark Bridger outside her home in Machynlleth, mid Wales, on October 1 last year.
The 47-year-old paedophile is serving a whole life sentence for killing the youngster.
A prisoner from HMP Wakefield was taken to hospital on 7 July. The incident is being investigated by the police.