Cornwall Partnership Trust was caring for five patients with coronavirus in hospital as of Sunday, figures show.
NHS England data shows no people were being treated in hospital with Covid-19 the same day the previous week.
Across England there were 1,526 people in hospital with Covid as of July 30.
Nationally, the number of hospital patients with Covid-19 has increased by 34% in the last four weeks.
The figures also show that six new patients with Covid were admitted to hospital in Cornwall Partnership NHS Foundation Trust in the week to July 28.