The report argues money saved from putting interest back on loans could be spent elsewhere, including raising or removing the cap on borrowing for living costs.
Money could also be pumped into improving secondary school education, the NZ Initiative argued.
The call to scrap interest-free loans has been repeatedly rejected by the National Government.
It also comes as Labour campaigns on scrapping tertiary fees completely for most students, and works on the idea of writing off existing debt for those who take certain public service jobs in the regions.
However, the call to consider the effect of interest-free loans has an ally in the Child Poverty Action Group.
The group released a report this month that said the zero-interest policy had the unintended consequence of allowing the government to put more of the cost of study on to students.
"It is good that interest is not compounding the debt and this makes the total amounts more tolerable. However, this fails to address the core issue of rising fees," the Laybying Our Future report stated.
"Student loans also privilege the wealthy, as those who are able to afford education are able to pay for their children's tertiary education while taking out the loan to accrue interest and repay at the slowest rate possible."
The action group's report concluded that insufficient income and support provided by government, family or available work meant students took on debt in addition to their student loan.
That included an overdraft, personal loan, credit card, and debt to families.
It recommended evaluating the trade-off between an interest-free policy and bringing back interest together with adequately funding universities and student support.
Currently around 180,000 people attend university.
In January, Labour leader Andrew Little announced in a State of the Nation speech in Auckland that Labour would provide three years of post-school study for every person in the country without a previous tertiary qualification.
And this month he revealed Labour was working on policy that would see graduates who take certain public service jobs in the regions get a chunk of their student loan wiped.
In 2014, the Government's share of the full cost of each student's tertiary education was 71 per cent, rising to about 82 per cent after the subsidy provided by interest-free borrowing is accounted for.
Tertiary Education, Skills and Employment Minister Steven Joyce has ruled out scrapping interest-free loans, but has said attempting to bring down fees through further Government subsidisation would be unfair on those who chose to enter the workforce rather than attend university.
The net cost of the student loan scheme - cash out, less repayments - last year was around $400 million. That was down from $771 million in 2009/10.
Joyce expects that trend to continue as the Government targets overseas-based borrowers who are in default on their repayment obligations.
Two such borrowers have been arrested at Auckland Airport as they attempted to leave New Zealand after returning temporarily.