Cornwall Partnership Trust was caring for five patients with coronavirus in hospital as of Sunday, figures show.
NHS England data shows the number of people being treated in hospital with Covid-19 by 8am on September 10 was up from four on the same day the previous week.
Across England there were 3,356 people in hospital with Covid as of September 10.
Nationally, the number of hospital patients with Covid-19 has increased by 43% in the last four weeks.
The figures also show that seven new patients with Covid were admitted to hospital in Cornwall Partnership NHS Foundation Trust in the week to September 8.