The woman, Farkhunda, 27, was savagely beaten and her body set ablaze in broad daylight, triggering protests around the country and drawing global attention to the treatment of Afghan women.
Police arrested 49 people in connection with the attack, including 19 police officers, some of whom were shown standing by doing nothing to stop the mob in cellphone videos recorded by bystanders.
In May a court sentenced four men to death and eight others were handed 16-year jail terms after a three-day trial broadcast live on national television.
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"The appeal court decided to reduce the sentence -- three of them got 20 years in prison and one 10 years," judge Nasir Murid, the head of the Kabul appeals court, told AFP without giving any further details.
The appeal was heard behind closed doors and reportedly reached a verdict on Wednesday, according to local media.
Farkhuda's brother Mujibullah told AFP the family had not been told of the court's decision or invited to the session.
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"We just heard through media that the appeal court in a secret session has reversed the decision. They didn't inform us. Whatever the decision is we will not accept it." he said.
Eleven Afghan policemen were also sentenced in May to one year in prison for failing to protect Farkhuda from the angry mob.
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