The Sensible Sentencing Trust is lobbying MPs to change the appeal process to deter criminals with a long history of convictions from making "frivolous" applications to the court.
Tony Robertson was sentenced to at least 24 years in jail last year for murdering Blessie Gotingco in May 2014.
Robertson argued he accidentally ran over Mrs Gotingco and then panicked, and he had no intention of raping or murdering her.
His appeal against the conviction and sentence was thrown out by the Court of Appeal on Friday.
It ruled there was no basis for Robertson's arguments, but accepted the initial car crash could have been accidental.
Sensible Sentencing Trust founder Garth McVicar said the Court of Appeal can increase a criminal's sentence in cases where an appeal is deemed frivolous, and that should have happened with Robertson.
Mr McVicar said MPs were being lobbied to introduce laws making it mandatory for an applicant's sentence to be increased in such cases. He said his organisation wanted one of the major political parties to pick up the idea and lobby on the trust's behalf.
Robertson would have been less likely to "waste the judges' time" if he knew the consequences of a failed appeal, Mr McVicar said.
"He's playing the game because he can. He has nothing to lose the way the appeal board have dealt with this. They have the law, they have the discretion to increase the sentence, but seldom do they do that, which is part of the problem."
That was one of the reasons the appeal courts were jammed solid and there were such lengthy delays around appeals now, said Mr McVicar.
"Taxpayers ... they fund the appeal courts, so I think we (will) get a lot of support from taxpayers, and MPs," he said.
Trust's suggestion "illogical" - lawyer
But criminal and human rights lawyer Golriz Ghahraman disagreed with the Trust and described the idea as illogical.
Ms Ghahraman, who has worked as a United Nations prosecutor, warned a law change could set a dangerous precedent and deter people from bringing appeals.
"It's illogical in that it may set a dangerous precedent, where legitimate appellants may be deterred from bringing appeals because we've said that if you're unsuccessful we may raise your sentence - not based on what you've done or sentencing considerations - but based on the fact that we think appeals are expensive."
She said being able to appeal a sentence was a fundamental right.
"Anything that relates to sentencing then comes from the Sentencing Act, and the jurisdiction of an appeal court to touch somebody's sentence on appeal, whilst they have that jurisdiction, has to relate back to considerations of sentencing law.
"The problem is conflating those two regimes. So when you're sentencing someone on appeal and a court wants to raise someone's sentence it has to relate back to considerations like the culpability of the person, the circumstances and seriousness of their offending and those are all defined in sentencing law.
"So to say that that jurisdiction should be used to punish people for some other thing they've done and specifically to punish them for bringing an appeal that might not have merit, would set a pretty dangerous precedent."
Ms Ghahraman said legitimate appellants could be put off from bringing appeals because considerations would be made on the basis that they were seen as expensive to conduct.
She dismissed the Sensible Sentencing Trust's example of Robertson, saying the case was an 'outlier'.
She said realistically 99 percent of appeals did not involve cases such as his.