Fortescue Metals Group founder Andrew Forrest expects his company will pay "little or no" minerals resource rent tax when it comes into effect from July 1.

Addressing the National Press Club in Canberra on Wednesday, Mr Forrest said the federal government's MRRT was not a "mining tax" but a penalty on junior mining firms and mineral explorers.

"I've been saying for a long time ... that we are going to pay little or no mining tax," Mr Forrest said.

"We are a largish company but we are nothing like the scale of the guys in that secret room that cut that deal (to axe the initial resource profits rent tax and bring in the MRRT).

"I would say we will pay between zero and $50 million of MRRT some time in the next five years - I am not sure when it is and it will depend on iron ore prices."

The non-executive chairman of the iron ore producer said the tax would not raise the estimated $10 billion suggested by the Government.