The patient died at Sandwell and West Birmingham Hospitals NHS Trust on Saturday, but their death was only confirmed today..
It was the first Covid-19 death at the hospital trust, which runs Sandwell General Hospital and City Hospital in Birmingham, since August 26.
It means the death toll at the trust now stands at 384.
The death toll in hospitals across the Black Country, Birmingham and Staffordshire stands at 2,575 – with 700 more deaths reported in care homes.
Across England a further 10 people have died of coronavirus.
More Covid-19 coverage:
A total of 983 patients have died at the University Hospitals Birmingham NHS Foundation Trust, which runs the Queen Elizabeth, Good Hope, Heartlands and Solihull hospitals.
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.
In Staffordshire, 355 people have died at the University Hospitals of North Midlands NHS Trust which runs the major hospitals in Stafford and Stoke.