Her mother Diana Parkes said Robert Brown is due to be freed in November even though he still “poses a great risk” to her family and other members of the public.
She is now urging Justice Secretary Alex Chalk to intervene and use his powers to refer the case to a parole board, so it can decide whether he should be freed.
Ms Simpson was killed by her estranged husband at their home in 2010, while their two children cowered in a nearby room. He hit the 46-year-old over the head 14 times before he wrapped her in a plastic sheet and buried her in a pre-dug grave in Windsor Great Park.
The former British Airways captain was acquitted of murder the following year, but admitted manslaughter on the grounds of diminished responsibility after claiming that he had been suffering from a stress-related condition called adjustment disorder.
The family of Ms Simpson, who was raised in York, have been told he will be released on licence, without facing a parole hearing, after serving half of his 26-year sentence.
"Action needs to be taken to block Robert Brown’s automatic release after only serving 13 years,” said Ms Parkes.
“His release poses a great risk to family and friends of Joanna Simpson also the wider public, especially women.
“Reliving my daughter’s brutal killing at the hands of Brown is emotionally exhausting. No mother should lose a child in such appalling circumstances. We all live in great fear.
"However we know that it is the only way to ensure that the Justice Secretary fully understands how dangerous Brown is."
The family have previously been told that Brown, who was moved to a low-security open prison in December, is classed as a “critical public protection case”, which means he will be closely monitored if he is released.
A Ministry of Justice spokesman said: “Joanna Simpson was brutally killed in a cowardly, senseless attack and needlessly taken from her family.
“The Lord Chancellor met with her loved ones in May and, as he reiterated on Sunday, will continue to give the case his close personal attention.”
Brown was acquitted of murder at Reading Crown Court in 2011, after the jury accepted that a condition known as “adjustment disorder” had substantially impaired his ability to exercise self control.
He was sentenced to 24 years for manslaughter and a further two years for an offence of obstructing a coroner in the execution of his duty.
During the trial, the jury was told that Brown had become consumed by anger because he believed he was not getting the divorce settlement he was entitled to.