Adnaan Hussain was returned to custody for 18 months after pleading guilty to breaching a restraining order over the calls made to the woman in August this year.
Hussain was previously locked up in June this year for a similar restraining order breach and carrying out criminal damage at the victim's home in Meanwood, Leeds.
The 31-year-old father-of four contacted the victim, who is aged in her 60s, on the morning of August 10.
Stephen Grattage, prosecuting, told Leeds Crown Court how the grandmother received the phone call at 8.30am but the caller did not say anything.
Mr Grattage said the victim could hear children's voices in the background and believed it to be Hussain's family.
The woman contacted police but said she was unsure if Hussain had made the calls as she believed he was still in custody at the time.
Police then informed her that he had been released from prison on licence at 8.30am on August 10.
Hussain, of South Street, Dewsbury, was arrested and denied the offending, claiming he was committed to rebuilding his relationship with his wife and children.
Mr Grattage said Hussain and the woman had formed a relationship in 2016 but she ended it in August 2017 when she found out that he had a wife and children.
He has committed a number of previous offences against the same woman, mainly for breaching restraining orders.
The restraining order, imposed in 2018, banned him from contacting the victim after he became possessive and controlling towards her.
Those offence's included Hussain trying to force his way into the woman's house.
He also threw a brick through the living room window.
The victim was isolating at the time due to the coronavirus.
Two days later the defendant went to the victim's house carrying a large bottle of vodka and knocked on the door.
Hussain started shouting through the letterbox, demanded his clothes back and threatened to throw the bottle at her pet dog.
The victim provided a statement to the court describing how the offending had sent her anxiety "through the roof" and she had suffered panic attacks.
She said: "He thinks he is above the law."
Glenn Parsons, mitigating. said Hussain continued to have problems with alcohol and drugs and pleaded guilty to the offence at an early stage.
The barrister said: "He knows he has to amend his ways.
"He knows he has to free himself of these demons."
Jailing Hussain, Judge Neil Clark said: "You have repeatedly pestered and harassed her.
"It seems clear to everyone that you should concentrate on your family rather than on your particular obsession with this complainant."
Hussain was made the subject of a further restraining order banning him from contacting the victim, without limit of time.