The plea follows plans released by investor Capital and Counties in March which reveal that there are no plans to include event facilities in the redevelopment.
As part of the plans Earls Court will be bulldozed, along with the 26 acres surrounding it to make way for 8,000 houses.
AEO chief executive Austen Hawkins said: "Earls Court is at the heart of London’s West End and attracts more than 2.5m visitors, 30,000 exhibiting companies and hundreds of events per year.
"Together with Olympia it supports £258m of expenditure in their boroughs and over £1.25bn in the London region. One in two Londoners visits the venues every year."
AEO chairman Douglas Emslie added: "The UK’s successful Olympic bid was based on its legacy commitment; however there are now plans to knock down one of the venues hosting the Olympics. It’s a legacy of destruction."
AEO is lobbying the national and local Government, the London Mayor, relevant planning authorities and Capital and County to ensure that the new development includes at least an exhibition centre.
Earls Court operator EC&O Venues recently revealed that Earls Court Exhibition Centre is in contract negotiations to run events until at least September 2012.