Black Country Healthcare Trust was caring for four coronavirus patients in hospital as of Tuesday, figures show.
NHS England data shows the number of people being treated in hospital for Covid-19 by 8am on August 24 was up from two on the same day the previous week.
There was one bed occupied by a Covid-19 patient four weeks ago in Black Country Healthcare NHS Foundation Trust.
Across England there were 5,911 people in hospital with Covid as of August 24, with 857 of them in mechanical ventilation beds.
The number of Covid-19 patients hospitalised nationally has increased by 14% in the last four weeks, while the number on mechanical ventilators has increased by 16%.
The figures also show that two new Covid patients were admitted to hospital in Black Country Healthcare NHS Foundation Trust in the week to August 22. This was the same number as in the previous seven days.