The father died during the blast at around 7pm last night and his son two hours later at the National Referral Hospital in Honiara.
The Solomon Islands Broadcasting Corporation reports the man's wife and another son, sustained serious injuries from the blast and are fighting for their lives at the hospital.
The blast also caused deafness in two other men.
The family members were sitting by a fire beside their house when the bomb, a remnant from World War Two, suddenly exploded from beneath the fire, killed the father instantly.
Earlier this month a 300 kilogramme bomb was safely removed from under another house in Honiara.
Local police told media that the owner of the dwelling had found the massive bomb while digging a hole to replace old floor posts.
On that occasion the bomb, thought to have been dropped by US forces during World War Two, was safely removed by the police explosive ordnance disposal team.
Photo file Solomon Times Caption:More than 100 unexploded ordinances were dug up in a residential area in Honiara.