Suffolk serial killer Steve Wright has lodged an application for an appeal.
Steve Wright was jailed for a whole life term
Wright, 49, was jailed for life last month after he was found guilty of the murders of five women, who all worked as prostitutes in Ipswich.
Wright's application for leave to appeal against the convictions has been sent to the Court of Appeal, Ipswich Crown Court said.
Brian Adams, the father of victim Gemma Adams, accused Wright of wasting time and money.
He said: "How much longer will he be allowed to continue wasting taxpayers' money?
"Judging by the overwhelming evidence against him and the speed with which the jury made up their minds about his guilt, it's just incredible that he would be allowed to make an appeal.
"It's about time he came clean and stopped wasting everyone's time."
Wright was sentenced after a six-week trial at Ipswich Crown Court where jurors unanimously found him guilty of all five murders.
The women were all found dead on the outskirts of Ipswich
The bodies of Ms Adams, Tania Nicol, Anneli Alderton, Paula Clennell and Annette Nicholls were found over a 10-day period near the town in 2006.
The naked bodies of the women, aged between 19 and 29, were found in December 2006.
Wright was given a whole life sentence and told he would spend the rest of his life in prison.
The BBC has seen the letter Wright sent to request an appeal in which he makes numerous points he claims are grounds for an appeal.
Wright alleges that the trial should not have been held in Ipswich, that his defence team did not represent him well, and that much of the evidence against him does not add up.
He also accuses the police of not adequately investigating other potential suspects.
"The prosecution alleged I had drugged all five women and then strangled them and yet there wasn't a shred of evidence found on myself, home or car relating to drugs.
"All five women were stripped naked of clothing/jewellery/phones/bags and no evidence was found in my house or car," he wrote.
Following the verdict some of the victims' families called for the death penalty to be reintroduced as punishment for Wright.
After the appeal was announced Wright's half-brother Keith Wright said: "...I can't see where he can get new evidence now.
"I don't want him to put everybody through it again if he is just trying to get out of it."