Poland is the largest of the 10 mostly eastern European countries that joined the bloc in May.
A survey released by pollster CBOS found that 70% of respondents supported the EU, up from 61% in January. It also showed traditionally eurosceptic farmers were warming to EU membership.
But only a quarter of respondents thought they had personally benefited.
"I would say this is an acceptance (of the EU) rather than enthusiasm. People don't want to be isolated. They are saying they may not benefit yet, but their children might. They are looking at the long-term," said Beata Roguska, of CBOS.
"People were expecting really drastic and negative changes. They were listening to anti-European politicians and weren't expecting good things. Now there is a great sense of relief. The shock of entering the EU was less than expected," she said.
Only 21% of poll respondents were opposed to the EU.
Asked whether they had personally gained from membership, 24% thought they had, while 31% said they had not.
Eurosceptic political parties such as the populist Self-Defence (SO) party led by the firebrand former pig farmer Andrzej Lepper, and right-wing Polish League of Families (LPR) gained support in the months leading up to Poland's entry.
But a poll for the daily Rzeczpospolita showed support for Self-Defence had halved since March. It now stands at 15%, behind LPR at 16% and the right-wing Civic Platform party at 24%.
CBOS's survey found more than 60% of supporters of Lepper's party and almost half LPR's supporters were pro-Europe, despite the policies of these parties.
CBOS, who surveyed 922 Poles in early August, also noted increasing support for the EU from farmers - traditionally eurosceptic because of fears that cheap imports will ruin their businesses.
Farmers are likely to get nearly 2 billion euros in EU subsidies in October - two months earlier than expected.
They have also benefited from soaring sales of meat and diary products, which has turned Poland into a net exporter of food. This week the government said Poland was heading for a hefty food trade surplus with the European Union in 2004.
The poll found EU support among farmers at 67%, up from about 50% at the start of the year. (Reuters)
