MindforYou provided eight holidays in its first year in 2015, 15 breaks in 2016 and said it expected its total number for this year to be higher.
The trips are usually taken up by couples.
They can stay at "dementia-friendly" accommodation in the Highlands, Perthshire, Fife and Lothian.
Locations in England and Wales are also available, the company said.
The main carer of people with dementia is often a spouse or another family member.
Val Johnston, of MindforYou, told BBC Radio's Good Morning Scotland programme: "In traditional respite care, the carer has a holiday and the person with dementia goes into a respite home.
"They are apart and some of these couples have been married for 60-plus years. They've never been apart before, so it can be a stressful.
"To come away on a holiday with your partner, I think, makes the person with dementia more at ease. They are not on their own."
A company that offers holidays that cater for people with dementia and their main carer has said it has seen increased demand for its breaks.