Birmingham Community 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 June 7 was up from two on the same day the previous week.
There were six beds occupied by Covid-19 patients four weeks ago in Birmingham Community Healthcare NHS Foundation Trust.
Across England there were 4,108 people in hospital with Covid as of June 7, with 116 of them in mechanical ventilation beds.
The number of Covid-19 patients hospitalised nationally has decreased by 44% in the last four weeks, while the number on mechanical ventilators has decreased by 34%.
The figures also show that 21 new Covid patients were admitted to hospital in Birmingham Community Healthcare NHS Foundation Trust in the week to June 5. This was down from 33 in the previous seven days.