At his trial prosecutor Sally Howes KC had said the father of four took out his “bad temper” on Zahra and bashed her head against a wall.
Jurors convicted Gholami of murder in a majority verdict of 10 to two and he was unanimously found guilty of child cruelty.
He has since appealed against the murder conviction.
Gholami’s case was that he came from from the shop and found his daughter already injured – his wife said she had fallen down the stairs.
Appeal judges dismissed his application, stating that there was no basis in his appeal for concluding that the conviction might be unsafe.
Gholami’s wife, Roqia, was cleared of murder during the trial but was also found guilty of child neglect unanimously by the jury.
During the trial, Zahra was described as a “bright, intelligent” child who was “highly curious” and wanted to find out about everything.
Ms Howes had said there was a “rivalry” between Zahra and Gholami’s “favourite son” and suggested the children had squabbled before the Tesco trip about going for ice cream and Gholami lost his temper with the little girl.
