Patrick Pritzwald-Stegmann (pictured), 41, suffered fatal head injuries when Joseph Esmaili struck him at Box Hill Hospital in Melbourne's east in May 2017

A Melbourne man who fatally punched a surgeon in the head at a hospital has been denied the chance to appeal his decade-long prison sentence.

Patrick Pritzwald-Stegmann, 41, suffered fatal head injuries when Joseph Esmaili struck him at Box Hill Hospital in Melbourne's east in May 2017.

Esmaili became the first person sentenced under the state's 'coward-punch' laws and received a mandatory minimum 10-year prison sentence.

Victoria's Court of Appeal on Thursday rejected his attempt to appeal that sentence.

Mr Pritzwald-Stegmann, a husband, father and dedicated heart and lung surgeon, was on his way home from work when he paused to ask a group - including Esmaili - to stop smoking near the hospital entrance.

A loud and aggressive row broke out, captured on CCTV.

The argument escalated and Esmaili, then aged 22, struck the surgeon in the jaw, knocking Mr Pritzwald-Stegmann unconscious.

He fell to the floor, hit his head and suffered a catastrophic brain injury.

Family switched off his life support a month later.

Esmaili's lawyers argued sentencing judge Elizabeth Hollingsworth made an error in considering whether Mr Pritzwald-Stegmann had been expecting the punch to the head and that Esmaili knew he hadn't expected it.

In a majority decision, Justices Phillip Priest and Emilios Kyrou disagreed.

'Mr Pritzwald-Stegmann's demeanour is entirely consistent with an individual endeavouring to deal with an angry, loudmouthed, uncouth lout, who was 'all talk and no action',' they said.

Esmaili's (pictured) lawyers argued sentencing judge Elizabeth Hollingsworth made an error in considering whether Mr Pritzwald-Stegmann had been expecting the punch to the head and that Esmaili knew he hadn't expected it

The doctor showed apparent calmness as he was confronted by Esmaili, who approached the surgeon with his hands behind his back.

'(He) then unleashed the dreadful blow suddenly and without any warning, at a time when Mr Pritzwald-Stegmann had his arms by his side, and in circumstances where he had no chance of defending himself,' they found.

In a separate judgment, Justice Michael Croucher said he would have granted Esmaili leave to appeal, but rejected the case.

Esmaili's attack might not fit the classic description of a coward's punch as a king-hit from behind to a victim who didn't have the slightest inkling of an impending attack, but it was still a 'low act' that was inevitably caught in the new laws, he said.

Esmaili was sentenced to a total of 10-and-a-half years after being found guilty of manslaughter and must serve 10 years before he's eligible for parole.