The cost of the extra refugees would be a "tiny fraction" of the Government's budget at $19.2 million over three years, she said.
"John Key has said increasing our quota won't do much, but it will make a massive difference to the extra people we take in - it will literally change their lives," Ms Roche said.
"[He] is using the excuse of not being able to help all the refugees in the world, as a reason not to help a few more."
Her bill will be placed in the ballot and compete with 74 other private member's bills to secure one of the few slots on the order paper and come up for debate.
There is support from across the political spectrum to increase the quota.
Labour, New Zealand First, Act, United Future and the Maori Party all want to see the refugee numbers increase by varying degrees.
NZ First's support would come only if immigration levels were cut at the same time.
There are currently about 52 million refugees around the world - numbers not seen since World War II.
Prime Minister John Key has said increasing the quota would not make enough difference to that situation, and it was better to focus on supporting the refugees we currently do settle.
New Zealand is ranked 87th in the world for total refugee resettlement per capita.
The Greens' member's bill comes amidst an ongoing controversy over the treatment of 65 asylum-seekers who were intercepted by Australian authorities while apparently trying to reach New Zealand.
The asylum-seekers and Indonesian authorities have alleged that the Australian authorities paid the people-smugglers thousands of dollars to turn around back to Indonesia.
The 65 refugees are now in a detention centre at Kupang in West Timor, and have directly appealed to New Zealand for help.
