The YouGov poll of 1192 people carried out during the last week shows that more than a third of Scots fear for the shipbuilding industry if Scotland becomes an independent nation.
In contrast, 18% feel shipbuilding would have a more secure outlook in an independent Scotland, while 29% think there will be no difference either way.
Just 5% reckon shipbuild-ing's future looks bright whether or not indepen-dence becomes a reality, with the rest "don't knows".
Deputy First Minister and MSP for Glasgow Southside, Nicola Sturgeon, said: "Over half of the respondents believe our shipbuilding industry will have a more secure future in an indepen-dent Scotland or there will be no difference, which dem-onstrates that the people of Glasgow and Scotland have seen right through the scaremongering of the Tory-led No campaign.
"An independent Scotland will have its own require-ments for Type 26 ships and offshore patrol vessels.
"And the UK government has just agreed with BAE Systems that Portsmouth will cease building ships in 2014, and that Glasgow is 'the most effective location for the manufacture of the future Type 26 ships.' That will remain true, whether there is a Yes vote or not."
Speaking on behalf of the Better Together campaign John Dolan, GMB Union convener at Scotstoun Shipyard said: "By far and away the biggest builder of ships in Scotland is the Ministry of Defence. The nationalists say that we can leave the UK but the MOD would still choose to build complex warships in Scotland. The simple fact is that this wouldn't happen."