The report, based on a YouGov poll of 799 employees, found 36 per cent have hidden their identity because they were afraid of discrimination - a figure that rises to 58 per cent for trans people.
Stonewall Scotland’s findings also highlight bullying as an issue, with one in six having been the target of negative comments or conduct from colleagues in the last year because they are LGBT.
Director Colin Macfarlane said: “Over the last few years employers across Scotland have shown real commitment to their LGBT staff by taking action to become more LGBT inclusive workplaces.
“However, our Work Report shows not every LGBT person feels supported by their employer.
“The fact that two in five trans staff have faced negative comments or conduct from customers or clients shows just how much still needs to change.
“Organisations who can ‘get it right’ reap the benefits of happy staff who will perform better.
“It’s been proven that diversity among staff leads to a more productive, positive and creative workplace environment.
“We need more organisations and businesses to ‘come out’ for LGBT equality and show their commitment to their LGBT staff and colleagues.”
The report shows trans staff tend to experience higher levels of negative comments or conduct, with 36 per cent experiencing it from colleagues.
There were 6 per cent who said they have been physically attacked by customers or co-workers in the last year because of their sexual orientation or gender identity.
One testimony said: “While serving a customer at work I corrected them on pronouns and they laughed in my face and asked me if I had a penis and told me I was wrong.
“My supervisor witnessed the whole thing and told me not to be so dramatic about it.”
Another told how they feel were excluded from post-work drinks, having never been asked, because they believe their colleagues fear negative reactions from their own friends.
Stonewall Scotland is calling for employers to develop zero-tolerance policies on homophobic, biphobic and transphobic discrimination and harassment, alongside communicating clear routes to report anti-LGBT bullying.
The charity is also calling for employers to take an active role in supporting trans staff by running awareness sessions for all employees on trans inclusion and developing a transitioning at work policy.