Solent NHS Trust was caring for nine 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 January 4 was up from five on the same day the previous week.
There were two beds occupied by Covid-19 patients four weeks ago in Solent NHS Trust.
Across England there were 9,332 people in hospital with Covid as of January 4, with 212 of them in mechanical ventilation beds.
The number of Covid-19 patients hospitalised nationally has increased by 70% in the last four weeks, while the number on mechanical ventilators has increased by 78%.
The figures also show that 12 new Covid patients were admitted to hospital in Solent NHS Trust in the week to January 2. This was up from three in the previous seven days.