Greig, who is a respected TV commentator now, spoke against the BCCI while delivering the 2012 MCC Spirit of Cricket Cowdrey Lecture at Lord's on Tuesday. This annual lecture is named after the late former England captain Colin Cowdrey.
"India is pre-occupied with money and T20 cricket and sees its IPL and Champions League as more important than a proper international calendar," Greig said in his lecture.
BCCI's IPL has brought millions of dollars to the game. This exciting format of the game has been a platform for youngsters to shine. However, some of the players have criticised IPL. But the popularity for IPL is still high.
Last year, Sri Lanka's Kumar Sangakkara was invited to deliver the Cowdrey Lecture.
The 65-year-old Greig added: "Much of the game is controlled by the BCCI because it controls enough votes to block any proposal put forward at the ICC board meetings. The reason for this is some countries would not survive without the financial opportunities India provides."
"What is just as disturbing is through the Champions League, South Africa and Australia have a partnership with India and are unlikely to risk offending India. The current Champions League 10-year contract generates just under a billion dollars and is 50% owned by India with Australia and South African sharing the rest. As a result of the dependence on India the process adopted by the ICC is simply not working."
Greig, however, did praise India for handing out one-time benefit for former players.
"We must acknowledge and praise India for embracing the spirit of cricket through the financial opportunities it provides, which has enabled a number of Test playing countries to survive, and some to thrive. World cricket would be in a sorry state if it weren't for the money shared with other countries from India's television deals.
"If there is proof of the leadership India can provide, it is the recent announcement of a one-time benefit payment of $13 million to former national and domestic players for their services to Indian cricket."