The man who raped and murdered Melbourne woman Jill Meagher has lodged an appeal against his prison sentences on two other rape convictions.

Adrian Ernest Bayley was already serving a life sentence when, in May, he was sentenced to 18 years in jail for three more violent rapes.

In those attacks, a Dutch tourist was raped in 2012 and two prostitutes were raped in separate attacks - one in 2012 and the other almost 15 years ago.

Bayley is appealing against two of the rape convictions and his new non-parole period.

He pleaded not guilty at all three trials.

At sentencing, he had his non-parole period extended to 43 years which would keep him in prison until he is at least 86 years of age in 2058.

The judge said Bayley was likely to die in prison.

Bayley on parole when he murdered Jill Meagher

The judge described Bayley's behaviour as serious and disturbing.

Bayley had a long history of violent attacks against women spanning more than 20 years.

He raped or attempted to rape three teenagers in separate attacks when he was 19 years old.

Bayley served his first stint behind bars in 1991 when he was sentenced to five years for sexual assault.

He served only 22 months of that sentence and later admitted to faking his way through a sexual offender rehabilitation program to gain early release.

In September 2000, he began what a judge described as a horrendous crime wave, raping six St Kilda prostitutes in a six-month period.

He was jailed for a minimum of eight years.