Samuel Brown set up 25 fake profiles in order to bombard his ex lover with threats and abusive messages.
-> Teenage boy stabbed in suspected arranged fight in LeedsA court heard Brown also offered members of the victim's family money to tell him of her whereabouts.
Leeds Crown Court heard Brown has a history of harassing people.
He is already the subject of a restraining order banning him from contacting another former girlfriend and his own grandmother.
Olivia Murray, prosecuting, told Leeds Crown Court the abuse began after their eight-month relationship came to an end.
Brown turned up at the the woman's home in Beeston, Leeds, and left a box containing two abusive letters.
-> 17-year-old Leeds girl stabbed to deathThe victim then blocked Brown from contacting her on Facebook.
He set up the fake accounts and sent messages which included "do you want me to kill you?" and "I wanna smack you."
Brown also wrote "You don't ignore me. When I see you, I'm going to bang you."
"You are dead. Your brother's dead.
"I'm going to find you, I'm going to kill you."
Brown continued to harass the woman for six months.
Police were contacted after Brown offered the woman's relatives money to tell him where she was.
He denied any offending when interviewed by officers, claiming the victim's account was "fictional nonsense."
Brown, of Woodhouse Grove, Huddersfield, pleaded guilty to harassment.
He has previous convictions for harassment and breaching restraining orders.
-> Police officers in dramatic high speed car chase through LeedsIan Cook, mitigating, said Brown has a history of mental health problems and struggled to cope with relationship breakdowns.
He urged Recorder Andrew Haslam, QC, to consider imposing a community-based punishment so Brown could continue to receive help to control his anger.
Brown was jailed for 14 months.
Recorder Haslam said: "You have a problem when it comes to someone ending a relationship with you.
"These were deeply unpleasant threatening messages that you sent.
"You threatened to tear her face off and threatened to kill her."