Its ranking of donations relative to wealth suggests Russia, France, and the US - the largest donor in monetary terms - should all be giving more.
Kuwait, Luxembourg, Denmark, Saudi Arabia and the UK lead the list of those donating sufficient money.
The United Nation's £3bn appeal for Syria is currently 44% funded.
Oxfam says that in the past few months many governments have pledged money in the wake of Syria's escalating civil war and refugee crisis, but it has then failed to materialise.
Oxfam's assessment is based on the sums sought by the UN, Red Cross and other appeals and the relative wealth and income of a group of 28 traditional big donor countries and Middle East states.
UK Prime Minister David Cameron has spearheaded demands for developed countries to contribute more money and Britain has spent more than £400m in total on aid for Syria and neighbouring states.
Oxfam says the UK's £149m to the appeals it has highlighted is more than one-and-a-half-times what could be expected.
In contrast, New Zealand has committed just 1% of what it should, Oxfam said. And Russia and Qatar, which have supplied arms to opposing sides in the civil war, have given only 3%.
Oxfam said other countries failing to get halfway towards their "fair share" included:
The commitments by Germany, the Republic of Ireland and Finland are on a level with what they should be expected to give, according to Oxfam.
The US has provided more than £512m but that is still less than two-thirds of what it should be based on its wealth, Oxfam said.
Kuwait was found to be the most generous donor, with its £200m more than four-and-a-half times its fair share. Norway and Sweden were also among the countries cited as generous donors.
Next Week the UN will launch another push for donations, arguing that Syria has become one of the worst humanitarian crises for decades.
The head of Oxfam's Syria programme, Colette Fearon, said: "While economic times are tough, we are facing the largest man-made humanitarian disaster in two decades and we have to seriously address it.
"The scale of this crisis is unprecedented and some countries must start to show their concerns to the crisis in Syria by putting their hands in their pockets.
"This is not the time for pledges. The situation demands committed funds in order to save lives."
More than 100,000 people have been killed since Syria's civil war began in early 2011, according to the UN.
Millions have fled the country and millions more have been left homeless.
Many countries have failed to donate their "fair share" to appeals to help tackle the Syrian refugee crisis, the UK-based charity Oxfam has said.