In the poll of more than 2,000 people, which was commissioned by the pro-life group, Where do they stand, seven in ten women wanted the limit reduced from the current 24 weeks to 20, and nearly six in ten wanted the limit reduced to 16 weeks.
The survey also found that nine in ten people questioned wanted sex selective abortions to be banned by the law.
The findings have been welcomed by the Evangelical Alliance. Its Head of Policy, Simon McCrossan, told Premier that the survey was timely: "This year marks 50 years since the 1967 Abortion Act was introduced and since then, over 8 million abortions have been performed, one in three women will have an abortion by the age of 45 and today for every four children born, one has been aborted.
"We don't believe that is the best care for women and for the unborn."
He says the survey shows that the dominant media narrative that the current abortion limit of 24 weeks is fine is not reflective of the views of women and society in general and therefore needs to be changed.
The survey also found that nine in ten people thought a woman considering abortion should have a legal right to independent counselling from a source that has no financial interest in her decision.
McCrossan added he believed the survey showed people's response to technology allowing views of the foetus in the womb: "For many people, it's now becoming difficult to reconcile a six-month cut-off point when you have images of foetuses at 12 weeks, which whilst not viable outside the womb, to many people look palpably human."
Listen to Simon McCrossan speaking with Paul Hagger: