In an online poll of 1,005 people by Censuswide Scotland, carried out in May this year, 207 (21 per cent) respondents said they are either not at all or are not completely open-minded and accepting of LGBT people.
Of the 630 women who took part in the survey, 112 (18 per cent) responded with that answer, while among the 375 men polled the figure was 95 (25 per cent).
Over-55s were the least open-minded and accepting age group, with 66 people (34 per cent) responding in that way.
Those aged between 16 and 24 years old had the lowest number of respondents who said they were not open-minded and accepting of LGBT people, with 13 of 122 respondents sharing that view.
The study also asked respondents whether other people would ever describe them as being homophobic.
It found around 13 per cent of men (47) and around 5 per cent of women (34) said they thought others could describe them as homophobic.
Jordan Ferguson, from Censuswide Scotland, said: "The Censuswide Scotland opinion poll has been tracking public attitude across a range of important issues in 2019.
"This particular study looked at how open-minded and accepting of LGBT communities respondents consider themselves, while also asking them to consider how they may be perceived by others.
"Our results found there to be a number of Scots who do not consider themselves open-minded and accepting of LGBT people.
"The responses vary across the age groups with the older respondents being the least likely to consider themselves open-minded."