University Hospitals Bristol and Weston 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 October 22 was up from four on the same day the previous week.
Across England there were 3,796 people in hospital with Covid as of October 22.
Nationally, the number of hospital patients with Covid-19 has increased by 21% in the last four weeks.
The figures also show nine new patients with Covid were admitted to hospital in University Hospitals Bristol and Weston NHS Foundation Trust in the week to October 20.