An estimated 40% of Irish internet users have received emails or phone calls trying to get access to their computer or personal details such as their banking information.
That is according to the latest Eurobarometer poll on the experience of cybercrime.
Nearly a third of Irish internet users have discovered malicious software on their device, but just over half of them have installed anti-virus software.
This compares with an EU average of 61% who have taken this precaution.
16% of Irish internet users - the third highest in the EU - say they have had experience of their social media or email account being hacked compared to an EU average of 12%.
Among the top concerns of Irish people are the misuse of personal data, security of online payments and online purchases.
While Irish people are more aware of cybercrime than the EU average, half of users do not take basic precautions such as changing their passwords every 12 months.
And while internet access in Ireland has never been higher at 80%, Ireland is behind Sweden (96%) the Netherlands (95%) and Denmark (94%).
Lowest access was in Romania (54%), Portugal (55%), and Greece (58%).