Harry Street was detained indefinitely in October after guns and explosives were found at his Birmingham home.
In 1978, then known as Barry Williams, he killed three people on the Bustleholm estate and later the owners of a petrol station in Warwickshire.
The 70-year-old died after a suspected heart attack at Ashworth Hospital.
A spokesperson for Mersey Care NHS Trust said a patient was admitted to the general hospital after becoming unwell but died at 09:49 GMT on Christmas Eve.
Two months ago Street admitted making an improvised explosive device as well as 50 homemade bullets.
Three handguns were also found at his home in the Hall Green area.
A serious case review is ongoing after police said they were initially unaware of Street's previous name or past convictions.
Sentencing Street, the judge at Birmingham Crown Court said he had "become obsessed" with his neighbours and harboured delusions they were harassing him.
Mr Justice Blair also drew comparisons with the 70-year-old's past, that saw him kill three neighbours in West Bromwich 36 years earlier.
He said Street had shown "similar behaviour to that which had preceded the terrible events of 26 October 1978".
Among other charges, Street also admitted one count of putting a neighbour in fear of violence between 2009 and 2013.
Street had been released in 1994 after serving 15 years at Broadmoor hospital for the 1978 shootings.
The spree started with him killing his neighbour George Burkitt and Mr Burkitt's son, Phillip, who were fixing a car on their driveway in Andrew Road.
Iris Burkitt became his next victim, before Street shot her daughter Gillian, who survived.
Neighbours Judith and Joe Chambers also survived, despite being shot multiple times.
Street then fled the scene in his Ford Capri, indiscriminately shooting as he left the estate.
Heading towards the East Midlands, he stopped at a petrol station in Nuneaton, where he shot dead the owners Lisa Di Maria and her husband Michel.
He was eventually cornered in Buxton, where police rammed his car before arresting him.
Almost 40 years on, Gillian Burkitt, now Gillian Dudley, was in the public gallery to hear sentence passed.
She celebrated with other victims as Street was told he may never be released.
A man who killed five people in a shooting spree which started in West Bromwich has died at a high-security psychiatric hospital.