The job involves upgrading a 2.8-mile single lane section of the trunk road to dual carriageway between Temple and Higher Carblake.
Improvements include widening and realigning the existing carriageway to provide additional lanes with central reservation and verges.
The successful firm will also construct three new grade separated junctions to replace the existing at-grade crossings with three new overpass bridge structures, a retaining wall, culverts and associated side roads.
The works are due to start in Autumn 2014 for an 27-month long build.
PQQs can be obtained from Mike McGowan, Cornwall Council. Tel: 01872323779.