Judge Geoffrey Grigson told Anthony Volney: "Yours was an act so callous as to be almost beyond belief. It is certainly beyond all understanding."
Dorian Lovell-Pank QC, for the prosecution, told the Old Bailey that Volney, 59, of Kilburn, north-west London, had thrown Sasha Davies over the balcony on 6 August last year in a fit of drunken rage.
"She fell seven floors to the ground. She was terribly badly injured. She never regained consciousness and died three days later in hospital, four days before her fourth birthday."
Volney - who denied murder - had been looking after his granddaughter and took her back to his flat after being asked to leave a local club, where he had caused trouble.
"He was not happy having been asked to leave. He was variously described as drunk, staggering, and was generally thought not to be fit to be looking after a small child," said Mr Lovell-Pank.
A witness said Sasha had been crying that she wanted to go home and her grandfather had been dragging her along the street and swearing at her.
A man living in Volney's block saw the final act. "He heard a child in distress and a man who was swearing a lot. He thought the girl sounded petrified. Every time she said something, the man would swear back and she would scream even more," said Mr Lovell-Pank. "There was one last scream, then he saw the defendant pick up the girl with both hands and drop her over the side of the balcony."Reuse content