Schürrer was found guilty on October 14 of bludgeoning to death a nearly four-year-old boy and his almost two-year-old sister and of trying to kill their mother in the central Swedish town of Arboga last March.
In a document filed with the regional Västmanland district court on Wednesday, Schürrer 's lawyer Per-Ingvar Ekblad appealed the verdict, charging it was invalid since one of the jurors had admitted to bias.
He called for the Swedish Appeals Court to "void the district court's verdict and return the case to the district court for a new trial."
One of the three jurors in the case, Cecilia Uggla, gave an interview to the Expressen tabloid at the end of the trial, saying she "has never really believed that she (Schürrer) is innocent."
She was removed from the case, but Ekblad argued that Uggla's statement indicated that she had been biased against his client from the beginning, which "goes against the presumption that the defendant is innocent until the opposite is proven."
He also stressed that the case against his client rested on largely circumstantial evidence, and that no DNA traces, finger prints or other technical evidence linked her to the crime scene.
The court had acknowledged as much in its verdict, but found there was "substantial other evidence that points to her," adding that she had been "in Arboga at the time of the crime and she has in the court's opinion given false testimony about her visit to Arboga that day."
The court also ruled a clear motive had been established.
The 23-year-old mother of the two murdered children, Emma Jangestig, is the live-in companion of a man Schürrer once dated.
The court ruled that several desperate actions by Schürrer leading up to the crime, including attempting to commit suicide and pretending to be pregnant with her ex-boyfriend's baby, proved she had not got over him and had a motive to attack his current companion and her family.