Ashok Kalyanjee pled guilty to murdering his six-year-old son Paul and three-year-old Jay in a car at a beauty spot near Lennoxtown in East Dunbartonshire in May 2008.
He was sentenced to life imprisonment and ordered to serve a minimum of 21 years by Judge Lord Brailsford, who described the murders as "awful".
The Scottish Criminal Cases Review Commission (SCCRC) has now reviewed the case and concluded a miscarriage of justice may have taken place.
It claims Kalyanjee may have been suffering mental health problems at the time of the crime and his subsequent court appearance.
An SCCRC statement said: "The commission has decided to refer the case to the High Court because the commission believes there may have been a mis-carriage of justice on the basis that it appears he may suffer from a mental dis-order which was undiagnosed at the time of his plea and which might have entitled him to plead that his responsibility was diminished.
"The Commission is also satisfied it is in the interests of justice that the case be referred."
Kalyanjee, a tourism student from India, killed the boys after collecting them from his mother.
He stabbed them several times with a large chef's knife before dousing their bodies and the car in petrol and trying to set it on fire.
The bodies were found in the car in the Campsie Fells after police were notified by a couple who saw Kalyanjee slumped over the wheel of his Mercedes.