The shadow education secretary wants the GCSE system updated to include academic and vocational subjects.
In a motion in the House of Commons, he will call for a "new political consensus" on education policy.
"We have a long-standing mismatch between the education system and the labour market," says Mr Hunt.
Mr Hunt is understood to want a more "constructive" approach to opposition after Labour's general election defeat.
The motion in the House of Commons will emphasise the common goals of wanting to improve education to drive economic growth and calls on the government to create a cross-party review "to cover exams, educational institutions and curriculum".
Mr Hunt wants to build a political consensus on moving away from the current GCSE system, which he argues needs to be overhauled when the leaving age has risen to 18 and these are no longer the final school-leaving exams.
The shadow education secretary wants a broader baccalaureate system incorporating both vocational and academic exams.
But such a change would need to be introduced over a longer period than the next Parliament - and Mr Hunt's move is an attempt to "begin a conversation".
Mr Hunt says that the exams system is no longer delivering the skills needed for the labour market.
"We need a new political consensus to put it right. That is why I am calling on the government to initiate a cross-party review of 14-19 education in this country.
"We should leave nothing off the table. Our only goal should be establishing consensus on the changes needed in our 14-19 education system to secure for our country the long-term economic growth and productivity that we need to succeed."
Education Secretary Nicky Morgan promised during the election campaign there would be no more "constant upheaval or constant change" in the next five years.
The major changes to the exam system and curriculum, announced in the previous coalition government, will be implemented during the next Parliament.
These include phasing in a more "rigorous" set of GCSEs and A-levels, with less coursework and modules and a greater emphasis on exams at the end of two years.
On Tuesday, the education secretary announced that the revised grading system for GCSEs would have a tougher pass mark than at present.

Jonathan Baines, 44, also known as "Willy", was found dead at a house on Ropery Road, Gainsborough, on 1 August.
Pamela McLaggan, 51, of Greystones Road, denied murder but pleaded guilty to manslaughter.
Prosecutors accepted her plea. She was remanded in custody at Lincoln Crown Court ahead of sentencing on 21 December.
The court heard Mr Baines had been out for the day at Market Rasen races before returning to Gainsborough and visiting pubs in the town.

The move is part of national fire service reforms unveiled by Home Secretary Theresa May last week.
Sussex PCC Katy Bourne said emergency services would have an increased duty to collaborate under the new bill.
But West Sussex County Council (WSCC) said it already had an excellent model.
East Sussex's fire authority said it would co-operate with the PCC but it believed collaboration could be achieved without elaborate structural change.
Ms Bourne said she had written to WSCC leader Louise Goldsmith and Phil Howson, East Sussex Fire Authority chairman, to request they begin to look at the feasibility of bringing both fire services under her authority.
"Just as we have one police force that effectively manages the county, we need to understand if one fire service not two could achieve the same," she said.
Ms Bourne's letter met with cross-party opposition from WSCC.
And Ms Goldsmith also invited the home secretary to visit West Sussex and see an alternative to the government's preferred plan.
Ms Goldsmith said West Sussex fire service was already integrated within the council and served communities.
She added last year's Shoreham air disaster showed how West Sussex emergency services already worked together.
East Sussex Fire Authority said it was willing to co-operate with the PCC to determine whether proposals could improve delivery of services and create efficiencies.
In a statement, it added: "[The fire authority] believes whilst close collaboration between the emergency services is essential, it can be achieved without elaborate structural change.
"It is also the fire authority's considered view that it is more accountable to the community it serves because its members are elected councillors."
Labour's Tristram Hunt is calling for a cross-party review to work on long-term changes to England's exams and curriculum for 14 to 19-year-olds.
[NEXT_CONCEPT]
A woman has admitted killing her partner who was fatally stabbed after returning home from a day at the races.
[NEXT_CONCEPT]
Plans set out by the Sussex police and crime commissioner (PCC) to take responsibility for fire services in East and West Sussex - and potentially merge them - have met with opposition.