At 11:53pm last night, police were called to a report of a man having been stabbed at an address in Bismarck Street, Beeston.
The victim, a 51-year-old man, was pronounced dead at the scene by ambulance staff.
A 57-year-old man has been arrested on suspicion of murder and is in custody.
A scene is in place at the address to undergo forensic examination.
The victim and suspect are known to each other.
The investigation is being progressed by detectives from West Yorkshire Police Homicide and Major Enquiry Team.