The Supreme Court of Canada will not hear the case of a man convicted of murdering his three sisters and another woman.

Hamed Shafia had asked the top court for leave to appeal, arguing new evidence showing he was a youth at the time of the deaths should not have been dismissed.

On Thursday, the SCC announced it will not hear the appeal, as usual giving no reason for the decision.

Shafia and his parents were found guilty in January 2012 of four counts of first-degree murder in the deaths of his teenage sisters and his father's first wife in a polygamous marriage.

The four bodies were found in the Montreal family's car at the bottom of the Rideau Canal in Kingston, Ont., in June 2009.

Shafia previously filed an appeal with the Court of Appeal for Ontario, alleging new evidence showed he was too young to be tried as an adult and should have been tried separately.

The appeal court found no reason to allow Shafia's new evidence, which it said was not compelling.

In his application for leave to appeal at the Supreme Court of Canada, Shafia's lawyers argue the appeal court was wrong and had not applied what is known as the Palmer test for admitting fresh evidence.