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"Number one, we have got to try and get the ICC right," Greig told the BBC in an interview.
"We have a situation at the moment where the ICC is dominated by India.
"They tell Zimbabwe, Bangladesh and one or two other countries what to do and they always get the vote.
"It's very hard, but somehow we have got to change things at that level."
South Africa-born Greig added: "We are playing too much cricket. I would be getting all the countries from the world and saying hey listen, what is this nonsense of giving Indian domestic cricket an open window?
"To give the IPL (Indian Premier League, a domestic Twenty20 competition) an open window, and reduce by two months the time available for cricketers to play around the world, in the current environment is just ridiculous.
"We have got to look very, very closely and make sure we do not destroy the cornerstone of the game which is Test cricket," said the 64-year-old former all-rounder, who settled in Australia after his playing days were over and has since enjoyed a long career as a television cricket commentator.
"It is laughable that (Chris) Gayle and (Kieron) Pollard are playing in the IPL when the West Indies are playing Pakistan - that is just ridiculous."
Greig, though, stressed his longstanding affection for Indian cricket, dating back to his time as a player which included leading England to a 3-1 Test series win in India in 1976/77.
"I took to India and the subcontinent very much...I loved the place," he said while giving an interview to coincide with the publication of a new biography, 'Tony Greig: A Reappraisal of English Cricket's Most Controversial Captain,' by David Tossell.
"It was the first time I really felt as if we were entertaining people, as the people there loved the game so much - to go to those stadiums and find them packed full," explained Greig, who made his name in England with south coast county Sussex.
"To this day (Kolkata's) Eden Gardens remains one of my top three grounds, just because of the incredible atmosphere."
