The death was announced at the University Hospitals Birmingham NHS Foundation Trust, which runs the Queen Elizabeth Hospital and others.
The patient died on September 15.
It means the total number of coronavirus deaths in hospitals across the Black Country, Birmingham and Staffordshire increased to 2,571.
A total of 980 patients have now died at the University Hospitals Birmingham NHS Foundation Trust.
More Covid-19 coverage:
At the Royal Wolverhampton NHS Trust, which runs New Cross and Cannock Chase hospitals, a total of 288 Covid-19 patients have died so far, and 230 people have died at Walsall Healthcare NHS Trust which runs Walsall Manor.
A total of 264 Covid-19 patients have died at Russells Hall Hospital, run by the Dudley Group NHS Foundation Trust, and 383 people have died at the Sandwell and West Birmingham NHS Trust, which runs Sandwell General and City hospitals.
In Staffordshire, 355 people have died at the University Hospitals of North Midlands NHS Trust which runs the major hospitals in Stafford and Stoke.
It comes as NHS England announced a further 18 people had died from coronavirus in hospitals, in figures announced on Thursday.
A spokesman for NHS England said: "A further 18 people, who tested positive for coronavirus (Covid-19) have died, bringing the total number of confirmed reported deaths in hospitals in England to 29,705.
"Patients were aged between 56 and 95 years old. All but two patients had known underlying health conditions.
"Date of death ranges from September 12 to September 16, 2020, with the majority on or after September 15.
"Their families have been informed."