Only 12% of people object to the move, which has been backed by the Scottish Government, while three-quarters of people believe that children should not be exposed to any tobacco marketing, according to the study by Cancer Research.
Anti-smoking campaigners say plain packaging will help tackle the product's "deadly allure" while discouraging young people from starting smoking. Public Health Minister Michael Matheson said the move is necessary to "build a generation free from tobacco". Alison Cox, Cancer Research UK's head of tobacco policy, said it was heartening to see the level of support.
She said: "Marketing can be the first hook that draws young people into a lifetime of nicotine addiction, an addiction that ends in death for half of all long-term smokers. Standardised packaging will give millions of children one less reason to start smoking."
Legislation to standardise cigarette packets is currently passing through the House of Commons under the Children and Families Bill.
The plans have already been openly supported by ministers at Holyrood.
The study found many Scots underestimate the number of smoke-related deaths, with around 100,000 people dying as due to smoking every year in the UK.