David Beasley warned that famine was possible in up to three-dozen countries and could overwhelm places already weakened by war such as South Sudan and Congo.
The former governor of South Carolina told the UN Security Council that more funding was needed to help "the 270 million people marching toward the brink of starvation".
And he said that £3.7bn was needed to feed the 30 million people who will die without the programme's assistance for a year.
"It's time for those who have the most to step up, to help those who have the least in this extraordinary time in world history," Mr Beasley said.
"Worldwide, there are over 2,000 billionaires with a net worth of eight trillion dollars (£6.1 trillion)."
He referred to reports that some of the wealthiest Americans have made "billions upon billions" during the pandemic. One study found that in the 11 weeks from mid-March when some US states entered lockdown, Amazon founder Jeff Bezos saw his wealth soar by £28bn, Facebook CEO Mark Zuckerberg's fortune surged by about £23bn and Tesla CEO Elon Musk's net worth rose by £11bn.
"I am not opposed to people making money, but humanity is facing the greatest crisis any of us have seen in our lifetimes," Mr Beasley said.
"It's time for those who have the most to step up, to help those who have the least in this extraordinary time in world history."
It comes five months after Mr Beasley warned of a potential "hunger pandemic".
He said that the response to his plea had kept people alive but set out the WFP's plan to reach as many as 138 million people this year - which he described as "the biggest scale-up in our history".
Mr Beasley referred to Congo, where instability already has forced 15.5 million people near starvation, and Yemen, where a lack of funding has forced cutbacks to aid.
In Nigeria and South Sudan, millions more people have become food insecure because of the pandemic, he said.
Mr Beasley told the security council that measures to contain the coronavirus must be balanced with the need to keep supply chains and trade moving across borders.
"There is a grave danger that many more people will die from the broader economic and social consequences of Covid-19 that from the virus itself, especially in Africa," Mr Beasley said.
"The last thing we need is to have the cure be worse than the disease itself."
Additional reporting by agencies