Pistorius was found guilty of the culpable homicide of Ms Steenkamp last month but he was cleared of murder.
Judge Thokozile Masipa is expected to hear legal arguments and testimony for several days before passing sentence.
Pistorius faces up to 15 years in jail, although Judge Masipa could suspend the sentence or only impose a fine.
She said the athlete had acted “negligently” when he shot his girlfriend through a toilet door , but in the “belief that there was an intruder”.
The Paralympic sprinter had strenuously denied murdering Ms Steenkamp after a row on Valentine’s Day last year, saying he shot her by mistake.
Karin Giannone looks ahead to the sentencing of Oscar Pistorius
Ms Steenkamp, a 29-year-old model and law graduate, was hit three times by bullets shot through a toilet door by Mr Pistorius at his home in the capital, Pretoria.
The judge said the state had failed to prove he intended to kill.
BBC.
