The couple and their three teenage children have been given a month to leave their council home after neighbours told of seven years of abuse, threats, property damage and noise.
Newport county court gave Torfaen CBC permission to repossess the family's four bedroomed house.
Clive Grace, chief executive of Torfaen CBC told the paper: 'Combating anti-social behaviour is a real priority. It is part of our commitment to improving the quality of life in Torfaen.
Director of housing David Burnell said: 'The council will take strong action in cases like this. The majority of tenants are excellent and we feel we have a duty of care to them.
'It isn't acceptable for such tenants to cause such problems for the majority, and this is an indication of the council's determination to act.'