The Irish Cattle Sheep Farmers Association wants to see higher payments for farmers who are most in need on poorer land.
It comes after it discussed the new arrangements for the ANC scheme in 2019 with Department of Agriculture officials yesterday.
An extra €23 million is being made available for the scheme, which the group says is a restoration of austerity cuts.
ICSA Rural Development Chairman Seamus Sherlock says they want farmers who have been left out to benefit.
"The concern is that a large number of people have been taken out of the scheme and we're very anxious that these people are given an adequate chance to appeal that decision," he said.
"We're also concerned that we have to see what level of funding is going to be given to each individual farmer, that the people who have been brought into the scheme are not just brought in at the bottom level."