Public Health Scotland data shows 27,070 people East Dunbartonshire had received both jabs by April 28.
That was up 5,725 compared to the previous week.
It means 30% of people aged 16 and over in East Dunbartonshire have now received two doses, using the latest Scottish population estimates.
Across Scotland, 1.2 million people had received both jabs 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 jab, 62% of thepopulation.
At the end of April, coronavirus restrictions were eased across Scotland, with the country moving from Level 4 to Level 3.
Everyone in the country is now also able to access rapid coronavirus testing, even if they have no symptoms.
Medical experts said the expansion of testing will help efforts to ease the country out of lockdown safely as it will be important to identify and prevent new outbreaks.
Chief Medical Officer Dr Gregor Smith said: “It may be tempting to think as vaccinations increase and cases drop, that testing will become less important.
"In fact, this will only make it more important to spot and prevent new outbreaks as cases emerge.
"We know from our experience of last summer just how quickly one outbreak can lead to another. This also applies regardless of whether you have been vaccinated or not.
"While the latest evidence suggests vaccines provide a high level of protection against the effects of Covid-19, they don’t yet provide a guarantee that you can’t still get the virus or pass it on to others.”
The data shows 2.4 million people aged 40 and over had received a first jab across Scotland – 85% of the age group.
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.
Following the first dose of the vaccine, a second jag is offered up to 12 weeks later.