The payments would be about $100 a week, but that figure would be flexible if circumstances changed.
As families bought equity, their payments to cover the Crown outlay would decrease.
They could cash it in at any time by selling it back to the Crown. The houses could not be rented out.
Greens co-leader Metiria Turei said the scheme would initially focus only on families with dependent children who are first-home buyers.
Servicing a mortgage on a $300,000 house at current interest rates costs more than $400 a week, which the Greens say is too expensive for 45 per cent of New Zealand families with children.
Eligibility criteria could include income and asset testing.
Mrs Turei said the scheme could dovetail with Labour's KiwiBuild policy. Labour housing spokeswoman Annette King said her party would be happy to work with the Greens and was pleased they acknowledged the KiwiBuild policy.
$300,000 house costs
Mortgage
$415 a week plus other costs (including rates, insurance) of $50 a week = $465 a week
Renting
$350 a week but no asset
Progressive ownership
Basic payment of $200 a week, $100 equity payment and $50 a week for other costs = $350pw. A family who increased the amount they spent on the home by the rate of inflation would own their home outright after 25 years.