© GettyThe incident took place in Manoa, a residential area of Honolulu.
The father, who has not been identified, is believed to have stabbed to death his wife and three children - aged 10, 12 and 17 - before taking his own life, police said.
Witnesses reported an argument at the home on early Sunday morning.
The deaths mark Hawaii's worst mass killing in over two decades.
Police initially responded to a call at 08:30 local time (18:30GMT) but left when no one answered the door, authorities said at a press conference on Sunday.
After receiving a second call less than an hour later, officers entered the home and found four people fatally stabbed.
The husband also was found dead and the cause of death remains under investigation, police said.
Police are still investigating a motive.
Honolulu's police chief Joe Logan said that the crime scene would have an impact on the responding officers "as it would on any officer, for the rest of their lives".
Nearby residents told local media that the family had lived in the area for about a decade. The children would often be seen playing outside.
"They are like a typical festival family. They dress up the house for the holidays and it's all normal," neighbourhood man Hiro Izumo told Hawaii News Now.
In a statement, Honolulu Mayor Rick Blangiardi said that the "inexplicable" tragedy had "shaken our community".
"Our heartfelt thoughts and prayers go out to the families and friends grappling with this profound loss," he said. "Let us stand together in support and solidarity during this difficult time."
Police said the killings represented one of the deadliest crimes in the state since the so-called "Xerox murders" of 1999, in which a suspect fatally shot dead seven co-workers.
Comment: See also: At least 55 killed with 1,000 people still missing as fire devastates Lahaina town in Hawaii (UPDATE)