Meanwhile, 13 percent oppose the plan and 23 percent are undecided, according to the study by researcher ARC Rynek i Opinia.
The poll was carried out from July 28 to August 3 on a sample of 1,037 respondents aged 18 to 65, Polish state news agency PAP reported.
Polish President Andrzej Duda said last summer that the country was taking "serious steps" to build its first nuclear power plant.
"Today we are taking some very serious steps to build nuclear power plants in Poland in order to protect the environment," Duda declared at the time.
The first unit of a new Polish nuclear power plant is expected to be put into operation in 2033, under a long-term energy policy adopted by the government last year.
Then further units are expected to come online every two to three years until a total of six, with a combined capacity of up to 9 GW, are in service, the PAP news agency has reported.
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Source: PAP