According to the poll, 53% would vote against joining the alliance at a referendum, and 32% would back membership.
Prime Minister Yulia Tymoshenko said on Saturday that a decision on whether Ukraine should join NATO will only be taken through a referendum.
In the survey, 51.9% of respondents said they viewed NATO as an aggressive imperialist bloc that would draw Ukraine into military conflicts.
Democratic Initiatives spokeswoman Irina Bekeshkina said the main reason why people do not want Ukraine to be a NATO member is their fear that the country's relations with Russia could be ruined.
The poll was conducted from December 5 to 18 last year. A total of 1,800 people were polled, with a margin of statistical error of not more than 2.3%.
Last week Ukrainian Foreign Minister Volodymyr Ohryzko handed a request for Kiev to join NATO's Membership Action Plan to the alliance's secretary general, Jaap de Hoop Scheffer.
The Russian Foreign Ministry warned on Tuesday that the country would have to take "appropriate measures" if Ukraine were to join NATO.