The survey was conducted in all of the country's 34 provinces in December 2009.
In 2009 only 51% of those surveyed had expected improvement and 13% thought conditions would deteriorate.
But in the latest survey 71% said they were optimistic about the situation in 12 months' time, compared with 5% who said it would be worse.
The other significant theme which emerges from the figures is growing antipathy towards the Taliban.
Ninety per cent said they wanted their country run by the current government, compared with 6% who said they favoured a Taliban administration.
Sixty-nine per cent believed the Taliban posed the biggest danger to the country, and 66% blamed the Taliban, al-Qaeda and foreign militants for violence in Afghanistan.
Most Afghans appeared positive about the presence of troops from Nato and other countries stationed in Afghanistan.
The survey also asked if people thought it was good or bad that US forces entered Afghanistan in 2001 to drive out the Taliban. Of those questioned, 83% said it was either very good or mostly good. This compares with 69% for 2009.
However, more of those questioned believe troops with the International Security Assistance Force (Isaf) are now worse at avoiding civilian casualties (43% worse and 24% better).
There was some ambivalence about how long Isaf forces should remain in the country - 22% said they should leave within the next 18 months, and 21% said they should stay longer than 18 months from now.
Afghans appear more positive about their general living conditions and the availability of electricity, medical care and jobs compared with a year ago.
Insecurity and crime were slightly worse, they said, and freedom of movement slightly better.
Despite a presidential election last year mired in controversy over ballot rigging, 74% said they were either very satisfied or somewhat satisfied with the outcome.
Also, 72% of Afghans rated President Hamid Karzai as excellent or good - compared with 52% 12 months ago - and 60% rated the performance of the present government as good or excellent, as opposed to 10% who thought it was poor.
One of the major issues facing Afghanistan is corruption among government officials or the police.
Of those surveyed, 95% identified it as a problem; 76% said it was a big problem and 19% said they considered it a moderate problem.
The survey was conducted by the Afghan Center for Socio-Economic and Opinion Research (Acsor) based in Kabul. Interviews were conducted in person, in Dari or Pashto, among a random national sample of 1,534 Afghan adults from 11-23 December 2009.
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