Colin McKay, 34, was found guilty of attacking the woman twice, raping a 15-year-old girl and indecently assaulting another female in West Lothian.
McKay had denied the offences but was found guilty after an earlier trial at the High Court in Edinburgh.
Sentencing him, Judge Lady Wolffe told him he had preyed on "vulnerable women".
She ordered that he be kept under supervision for a further two years and be put on the sex offenders register.
McKay was found guilty of raping the mother on two occasions at her home in the summer of 2005 and raping the teenage girl the same year at a house in West Lothian.
The court heard that he turning up at the first victim's door and attacked her after removing the baby from her arms.
He was also convicted of carrying out the indecent assault on the third victim at a house in Armadale in 2011.
The judge said that the case disclosed him to be "a predatory sexual offender preying on vulnerable women when the opportunity arose".
Lady Wolffe said: "You have been convicted of a number of predatory rapes of women who were vulnerable by reason of their age or circumstances."
She told McKay he had been assessed as posing a high risk of further violent offending.
She added: "You are noted as adopting a position of extreme denial and blame your victims."
Defence counsel Ian Duguid QC said: "His evidence was to deny categorically that any of these allegations took place."
But the defence counsel acknowledged that a jail sentence was "inevitable" following his conviction for the offences.
Mr Duguid said the proceedings had been a "chastening" experience for McKay and added: "He is unlikely to be involved in any kind of this activity in the future."
A man who raped a mother moments after taking her baby from her arms has been jailed for eight years.