Chris Ashford of Teamsters Local 927 said the union would submit a brief to Labour Minister Norm McFarlane this week asking for an amendment to the provincial Labour Relations Act.
The law does not affect New Brunswick-based truckers who operate outside the province, because they are federally regulated.
Ashford told a local newspaper that dump-truck drivers are hurt the most since they rarely, if ever, leave New Brunswick for work. A unionized driver would be paid between $51 and $63 an hour while independent operators make anywhere from $28 to $40. While that may seem like a good wage, Ashford added that drivers must pay their own fuel, insurance, and maintenance costs.