A poll by the Uutissuomalainen news group suggests that one third of respondents would oppose Finland accepting child refugees currently in camps in Greece.
Two in five respondents, on the other hand, supported the plan. One in five did not have an opinion either way.
Those aged 30-44 were the most negative about the idea while the over-70s were most positive about taking in the children.
One week ago the government decided to take in 175 asylum seekers from camps in Greece and elsewhere in the EU.
President Sauli Niinistö said afterwards that Finland should prioritise children when selecting asylum seekers for resettlement.
There are currently around 40,000 asylum seekers in refugee camps on the Greek islands.
The survey was conducted by Tietoykkönen on behalf of Uutissuomalainen. They interviewed some 1,000 Finns and the margin of error was +- 3.1 percentage points.