The NBRU is calling on the Minister for Transport, Shane Ross to establish a dedicated transport police to deal with violence and anti-social behaviour on trains.
Over 1,000 incidents have been logged by Irish Rail over the past two years and the figure is rising.
Records obtained by the RTÉ This Week programme report problems with aggressive behaviour, criminal damage, fighting and attacks against staff.
The National Bus and Rail Workers Union believes the real number of incidents is actually much higher than the official record.
NBRU chief Dermot O'Leary says they have written to the Minister for Transport, asking him to establish a dedicated transport police like the model used in the UK.
He said: "Some of the incidents that are happening these days unfortunately are not being reported.
"The underlying point is that there is a lot of anti-social behaviour and a lot assaults on staff members.
Irish Rail has confirmed that over 1,000 incidents of anti-social behaviour have been logged on trains since the start of last year.
That includes aggressive behaviour, fighting, criminal damage, and attacks on staff.
The company's Barry Kenny says they have increased security to deal with the problem.
He said: "We have 45.5 million passenger journeys a year so obviously the vast majority of people travel without incidents.
"We have increased our security resources to help deal with anti-social behaviour with 21% more now than two years ago."
- Digital Desk