Public Health Scotland data shows 37,114 people Falkirk had received both jags by April 28.
That was up 7,719 compared to the previous week.
It means 28% of people aged 16 and over in Falkirk have now received two doses, using the latest Scottish population estimates.
Across Scotland, 1.2 million people had received both jags by April 28, 26% of the population.
That was an increase of 266,000 from the week before.
The data also shows that 2.8 million people across Scotland have received a first jag, 62% of the population.
This week coronavirus restrictions were eased across Scotland, with the country moving from Level 4 to Level 3.
Public Health Scotland's vaccination rollout began on December 8, with doses given first to care home staff and residents, frontline health workers and the older age groups.