The Britannia Bridge has seen traffic increase 21% in five years
The majority of people consulted over plans to improve transport links between Anglesey and the mainland favour the building of a new bridge.
Deputy First Minister Ieuan Wyn Jones announced the findings at the island's annual agricultural show.
The consultation exercise listed four options - widening the existing bridge, building a new multi or single span bridge or taking no action.
70% of the 1,000 responses called for some form of new bridge.
The existing Britannia Bridge carries the A55 from the mainland to Anglesey.
It saw a 21% increase in traffic between 2002 and 2007.
Mr Jones said: "The A55 provides the main economic artery for north Wales and links Ireland to the European continent - its enhancement and development is essential.
"We gave the public an opportunity to have their say on the future of the Britannia Bridge and 70% have called for some form of new bridge.
"I am announcing today an investigation into the technical options for a new bridge and to consider the environmental issues we face.
"This will look into what is possible and give us some broad cost estimates."
Of those who responded 94% believed improvements were necessary.
The Menai Strait was first bridged in 1829, with Thomas Telford's famous suspension bridge.
The Britannia Bridge was built by Robert Stephenson in 1850 to carry rail traffic and a road deck was added in the 1970s.