In 2011 there were 841,053 Catholics in the country, an increase of 4 per cent since 2001.
This means that Catholicism remains the second largest religion after the Church of Scotland.
However, figures for the Church of Scotland fell during the same period, from more than 2.1 million to 1.7m, while the number of Christians overall also fell, from 3.3m to 2.8m.
Professor Tom Gallagher, an expert on Scotland and Christianity, said he attributed the stability of Catholic population to the large-scale arrival of Poles in Scotland.
"Perhaps it is also the case that Catholics who drift away from regular participation in their faith are much less inclined to renounce it altogether, compared to other Christian faith communities," he added.
Some leading church figures have suggested that the scandal over the departure of Cardinal Keith O'Brien earlier this year, after allegations of sexual misconduct, may have affected the standing of the Catholic Church in Scotland.
"It is too early to say how wounded the Church is," said Professor Gallagher, whose latest book is Scotland Divided: ethnic friction and the Christian crisis.