The homeless man who brutally raped and murdered pasty chef Renea Lau in Melbourne's Kings Domain has been jailed for 33 years.

Supreme Court Justice Betty King said on Friday that what Scott Allen Miller did to Ms Lau was every woman's and every parent's worst nightmare.

Renea Lau

Justice King said Melbourne was usually a very safe place to live, with the number of murders having dropped from 135 in 2005-06 to 82 in 2013-14, but Miller's crimes had left women feeling less safe and

secure when going about their normal day to day lives.

The judge said Ms Lau would have felt safe when walking on the well-lit St Kilda Road to Flinders Street station on her way to work just after 5am before Miller, a complete stranger, passed her in the street and killed her in a "brutal and sadistic manner".