NHS England figures show 257 people had died in hospital at Gloucestershire Hospitals NHS Foundation Trust as of 5pm on Sunday (November 29).
That was an increase of six compared to Friday, when there were 251.
It means there have been 23 deaths in the past week, up from 22 the previous week.
The victims were among 1,753 deaths recorded across the South West.
Daily death counts are revised each day, with each case backdated to the actual date of death.
This means some of the deaths that were first recorded in the latest period may actually have taken place days earlier.
NHS England guidance states: “Confirmation of Covid-19 diagnosis, death notification and reporting in central figures can take up to several days and the hospitals providing the data are under significant operational pressure.”
Only deaths that occur in hospitals where the patient has tested positive for Covid-19 are recorded, with deaths in the community excluded, such as those in care homes.