Mr Johnson is calling for a "root and branch" examination of the system
Gordon Brown should hold a national referendum on electoral reform, Health Secretary Alan Johnson has said.
The prime minister should offer the public a "genuinely radical alternative" to the present system, he wrote in the Times.
A referendum could be held on the same day as a general election, said Mr Johnson, who has denied his reform call is part of a Labour leadership bid.
The Electoral Reform Society said his idea was "a breath of fresh air".
'Overhaul the engine'
Mr Johnson, who has been widely tipped as a potential successor to Mr Brown, urged the prime minister to involve the public in "a root and branch examination" of the political system in order to regain trust following the expenses scandal.
"We need to overhaul the engine, not just clean the upholstery," he wrote.
Under the current system, sometimes called "first past the post" or "winner takes all", the successful candidate is the one with the most votes, with no requirement for them to gain an absolute majority.
But Mr Johnson said the government had the mandate to change that and should hold a referendum on "a specific new system".
However, the heath secretary later revealed he did not clear his article outlining his proposals with the prime minister before publication, although he said he did discuss it with people close to Mr Brown.
And he denied his call for a referendum was part of a bid for the Labour leadership.
"No, and it's quite unfair to suggest that it is. It is absolutely nothing to do with that," he told BBC Radio 4's The World At One.
The system Mr Johnson favours is known as Alternative Vote Plus
The new system Mr Johnson favours is known as Alternative Vote Plus and was first suggested by the Independent Commission on Electoral Reform, led by Lord Jenkins, in 1998.
Under AV Plus, voters would have two ballot papers: one for their constituency representative and a second for their favoured political party.
Most seats in the Commons would be filled with locally elected MPs, but the remainder would be allocated by proportional representation according to the number of votes cast for each party.
Calling this an "elegant" option, Mr Johnson said: "This is a genuinely radical alternative that only Labour in government can facilitate."
Speaking to the BBC, he said the review of the voting system would be part of a fundamental examination of the political system.
"We're going to look at fixed term parliaments, reform of the House of Lords, more power for Parliament over the executive," he said.
Energy Secretary Ed Miliband: "We need to go beyond reforming our expenses"
Climate Change secretary Ed Miliband later said he agreed that any reform of the political system needed to go beyond the issue of expenses.
"We need to have a much wider debate in Britain about how a Parliament works, how we elect our representatives and how we can transform more power to people themselves," he said.
Dr Ken Ritchie, chief executive of the Electoral Reform Society, said Mr Johnson should be congratulated for speaking out about the need to overhaul the "decrepit first-past-the-post system".
"His proposal... is a breath of fresh air in the debate on MPs' expenses that risks turning into a cul-de-sac," Dr Ritchie said.
The idea of proportional representation is simply not popular in our party, it's not popular in the Tory party, and even if there was a referendum held, it would not be binding
Labour MP Sir Stuart Bell
UK Independence Party leader Nigel Farage said Mr Johnson seemed to be the only Labour politician who had got the issue right.
"What the laws are, that's properly the province of Parliament, however elected. But how the laws are made is something that must be put to a referendum," he said.
But Sir Stuart Bell, Labour MP for Middlesbrough, said Mr Johnson's electoral reform proposals had little support in the House of Commons and would never be implemented.
"The idea of proportional representation is simply not popular in our party, it's not popular in the Tory party, and even if there was a referendum held, it would not be binding," he said.
"It could only be consultative, and a sovereign Parliament, elected after the next election, would simply ignore it."
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