Carrying what appeared to be a sawn-off shotgun and a machete, the four men broke through the patio doors at the home on Low Moor Side Lane, New Farnley.
A safe containing jewellery was stolen after women and a 12-year-old girl were assaulted during the raid at 11pm on Tuesday.
Detective Sergeant Al Burns, of Leeds District Crime Team, said: “This was an absolutely terrifying ordeal for this family to be confronted and attacked by armed men who had broken into their home late at night.
“There were young children involved and the victims have been left very badly traumatised.”
In the home at the time were two women, aged 36 and 57, a 64-year-old man, and three girls, aged eight, 10 and 12.
The culprits confronted the younger women and roused the other occupants from their beds.
They tied up the man and demanded to know where the safe was.
Both women and the 12-year-old girl were assaulted and pushed around and the older woman had jewellery pulled from her wrist.
The two women were later treated for minor injuries by ambulance staff.
The men searched the house before taking a safe containing jewellery.
They stole a blue Volvo V70 estate from the driveway and drove off.
An iPhone stolen during the robbery was found dumped some distance away in Back Lane.
The stolen Volvo was found abandoned at about 5am in Broadlands Court, Pudsey. It has been recovered for forensic examination.
Det Sgt Burns said: “This was clearly an offence that was planned and targeted at this family.
“We are carrying out extensive enquiries and would like to hear from anyone who has any information that could assist the investigation.
“We are keen to speak to anyone who may have seen the men acting suspiciously in the area or saw them dumping the car in Broadlands Court in Pudsey.
“The safe has not yet been recovered and we would like to hear from anyone who has found.”
Anyone with information is asked to contact Leeds District Crime Team via 101 quoting log number 1889 of September 27 or call the independent charity Crimestoppers anonymously on 0800 555 111.