Somerset County Council's Northern Inner Distributor Road (NIDR) was meant to be completed by March 2014.
The council has blamed the delay on a bridge being redesigned but did not confirm if costs will go up. The road will now open at the end of next year.
Independent county councillor Mike Rigby said: "Clearly something's gone horribly wrong with the project."
The project will link the west and east of the town.
The council said piling work had begun for the Kingston Loop bridge, which goes over Station Road.
A council spokesman: "Some progress has been visible but much of the recent work to revise the design of the bridge over Station Road has been taking place behind the scenes.
"This is now complete and we are entering the final phase of the project, with work on the bridge having started this week."
The BBC understands the delays were caused by engineering problems with the disused bridge.
The council also declined to confirm whether the delay would mean increased costs for the project.
Mr Rigby has been investigating the cause of the delay for the past year.
He was told by the council he needed to sign a confidentiality agreement before the reasons were disclosed.
"I've asked the question repeatedly about what's going on, and I can only be told if I sign an agreement making me promise I won't tell anyone when I find out," added Mr Rigby.
The roads project is linked to the planned regeneration of the Firepool area in Taunton, which relies on the new road for bringing better access.
Planning permission has now been submitted for a new cinema, hotel, shops and housing for Firepool.
A Somerset politician has cited concern over delays and increasing costs of a £21m road scheme in Taunton.