Solent NHS Trust was caring for 17 patients with coronavirus in hospital as of Wednesday, figures show.
NHS England data shows the number of people being treated in hospital with Covid-19 by 8am on March 8 was up from three on the same day the previous week.
There were six beds occupied by patients with Covid-19 four weeks ago in Solent NHS Trust.
Across England there were 7,655 people in hospital with Covid as of March 8, with 166 of them in mechanical ventilation beds.
Nationally, the number of hospital patients with Covid-19 has increased by 20% in the last four weeks, while the number on mechanical ventilators has increased by 42%.
The figures also show that 11 new patients with Covid were admitted to hospital in Solent NHS Trust in the week to March 6. This was up from two in the previous seven days.