The blaze was reported at about 07:30 BST on Saturday at the unoccupied semi-detached house at Wolfhill Link.
A 78-year-old woman and a man, 76, who is disabled, had to leave their home which has been damaged.
It is understood youths lit a fire in the derelict house which got out of control.
No-one was injured in the blaze which police are treating as arson.
The couple's granddaughter, Emma McKee, said a neighbour woke her to tell her about the fire.
"Over the last year or so, my granny and granddad have constantly complained about the kids knocking about the area and lighting fires. There were lampposts and glasses smashed outside their house," she said.
"At about 7.30 this morning, my granddad heard noises from the house next door which is abandoned.
"They got dressed. They thought there were people there. They saw four boys running with their hoods up. Then my granny saw the smoke and phoned the fire brigade."
She said all four bedrooms in her grandparents' home had been damaged and there was water damage throughout the house.
"All the memories are in that house. They've been there for 30 years . It's something they built together. They might have to move out now," she said.
"My granny is the nicest woman you'll ever meet. She is completely heart broken. She has been going through this for a while and has not been sleeping. My granddad is angry. He couldn't do anything."
The house next door to the couple has been derelict for about 10 years.
Twenty firefighters tackled the blaze. Police are appealing for information.
An elderly couple may have to leave their north Belfast home after a fire was started in the empty house next door.