The number of tourists coming here was up 4.2% for January to June this year.
Tourism Ireland say this was the best ever month of June for Irish tourism - with almost one million arrivals.
Visitors from North America were up by 21.6%, and numbers coming from Mainland Europe grew by 5.9%.
But the number of tourists popping over from Britain dropped back by 6.4%, to 1.745 million visits.
Tourism Ireland chief Niall Gibbons says Brexit fall-off could be to blame.
"The decline in the value of sterling has made holidays and short breaks here more expensive for British visitors.
"And economic uncertainty is undoubtedly making British travellers more cautious about their discretionary spending."