It would be built above the plinth where the original Crystal Palace, created by Joseph Paxton to house the 1851 Great Exhibition, stood. It burned down in 1936.
The design was unveiled at a meeting of the park's working group, comprised of 80 organisations, on Thursday.
Philip Kolvin of the Crystal Palace Campaign, which fought to save the top part of the park from being turned into a 20-cinema multiplex, approached the architect Chris Wilkinson 18 months ago to create a design.
Mr Kolvin: "It's amazing, I just approached my design gurus and told them I had no money and would they like give up a year of their time to help? And they did.
"They wanted to be involved in an exciting project.
"The response was really positive from the majority of people at the meeting.
"Some people say it doesn't look like the original palace but it comes back to the architectural debate - do we create a pastiche of the past or do we look to the future?"
The designers want the building, which they say will house the biggest room in London and give visitors views across the city, to echo the original glass building but use up less of the park's open space.
There will be two floors, the biggest of which is 4,500 square metres.
One level would be used for a variety of exhibitions and would contain a 150 metre long dome hall devoted to sculpture.
The second would contain bars, restaurants and a function room.
The building will be the centre piece of a sculpture park.
Chris Wilkinson said: "This will be an iconic building of the 21st Century. It will be the first building of its kind in the world."
Camden-based artist Antony Gormley who designed the Angel of the North sculpture has had an input and backs the plans.
The funding for the project would need to found through fundraising, corporate sponsorship and grants.
Bromley Council, which is part of the working group, will now study the plans.