Birmingham Community Healthcare Trust was caring for 12 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 2 was down from 15 on the same day the previous week.
There were no beds occupied by Covid-19 patients four weeks ago in Birmingham Community Healthcare NHS Foundation Trust.
Across England there were 10,177 people in hospital with Covid as of August 2, with 240 of them in mechanical ventilation beds.
The number of Covid-19 patients hospitalised nationally has decreased by 8% in the last four weeks, while the number on mechanical ventilators has increased by 5%.
The figures also show that 42 new Covid patients were admitted to hospital in Birmingham Community Healthcare NHS Foundation Trust in the week to July 31. This was up from 37 in the previous seven days.