The former education secretary argued the final Brexit decision should be given back to the people and out of the hands of "deadlocked politicians".
She called for three options to be on the ballot paper: the prime minister's Chequers deal, staying in the EU or a clean break from Europe with no deal.
The UK is due to leave in March 2019.
Ms Greening, who resigned after the cabinet reshuffle in January, said the referendum should offer a first and second preference vote so that a consensus can be reached.
Speaking on BBC Radio 4's Today programme, Ms Greening said the government's proposals were a "genuine clever attempt at a compromise that could work" but "suits no-one".
The MP for Putney said: "The reality is Parliament is now stalemated. Whatever the proposal on the table, there will be MPs who vote it down. But Britain needs to find a route forward."
Ms Greening, who supported Remain in the EU referendum, is the highest profile ex-Cabinet minister to call for a second referendum.
She said there were other senior Conservatives who agreed with her stance, adding that people who supported Leave in the referendum would also feel the government's approach is "not what they voted for".
In her article in the Times, she lambasted the PM's Brexit blueprint, saying: "We'll be dragging Remain voters out of the EU for a deal that means still complying with many EU rules, but now with no say on shaping them.
"It's not what they want, and on top of that when they hear that Leave voters are unhappy, they ask, 'What's the point?'
"For Leavers, this deal simply does not deliver the proper break from the European Union that they wanted."
No comments: