The demand for extra school places should be a "golden moment" to open more "innovative" schools, says Labour's Tristram Hunt.
This could mean school leaders from high-performing countries such as Singapore or Finland opening new schools in England, he says.
Mr Hunt says he wants to move away from the "narrow, exam factory vision".
A Department for Education spokesman said the curriculum was already innovative and "world leading".
The shadow education secretary will tell the ASCL head teachers' conference: "I want the best school innovators in the world - be they from Australia, America, Singapore or Finland - to come and open up new schools in our coastal towns, rural market towns and coalfield communities.
"We simply cannot afford to be parochial when underperformance needs to be tackled,"
"We have to change. We have to chart a course away - carefully, slowly, consensually - away from the narrow, exam factory vision of recent years," he will tell head teachers.
"England's demographic surge affords us a tremendous opportunity to do something different."
Mr Hunt says he wants technology and different ways of learning to challenge the "industrial model of schooling".
Mr Hunt will also call for more parental involvement in their children's education.
Labour has called for the scrapping of the free schools programme, but Mr Hunt says he wants to encourage "parents, teachers, businesses and voluntary groups to set up schools in areas of need".
He also wants academies to be able to change academy chains if parents are dissatisfied and he wants parents to be able to play a bigger role within trusts running chains of schools.
But a spokesman for the Department for Education said: "Thanks to our plan for education more children in England have the opportunity to go to a good or outstanding school than ever before and free schools have been crucial to that change.
"A recent survey revealed how free schools are bringing new ideas and approaches to education - with 84% collaborating with neighbouring schools or planning to, two-thirds offering an alternative to the national curriculum in some or all subjects; and around half providing an extended school day.
"We have introduced a world-leading new computing curriculum. England is one of a handful of nations to make coding and computer science compulsory from age five."
A Conservative spokesman said: "This is yet more chaos from a party with no plan for England's schools.
"Just the other week Ed Miliband attacked the 'alphabet soup' of schools in this country while pledging to bring them all back under local council control.
"Yesterday Ed Balls let slip that Labour wants to close free schools altogether. Now Tristram Hunt wants a whole different set of schools but doesn't seem to trust parents and teachers in this country to lead them."
The conference in London will hear warnings about funding from ASCL's president, Peter Kent.
He will tell the gathering of head teachers that children's education should not be "sacrificed" by austerity - and that schools are already struggling with inadequate budgets.
"The reality is that our current system of funding is making it impossible for some schools and colleges to make ends meet," says Dr Kent.
"Too many institutions are having to grapple with the reality that the level of funding is not enough to sustain the quality of education that our children deserve.
"Our children only get one chance and will not understand if we tell them in five years' time that their education has been sacrificed on the altar of deficit reduction."