Pontio at Bangor University was due to open in September and is largely being paid for with public funds.
The worker claims building mistakes and extensive water damage are responsible for delays and pushing it over budget.
Construction firm Galliford Try said challenges were not out of the ordinary and were being met to deliver a "high quality" building.
The Pontio arts and innovation centre is due to include a theatre, cinema and innovation and creative hub linked to the university.
Photos obtained from inside the building in Bangor reveal some of the problems.
Newly-laid floors have been dug up and recently finished walls and ceilings hacked apart because of extensive water damage.
Staircases, basement rooms and the arts centre's new cinema have all suffered damage.
The worker told BBC Wales: "You get sent to do something in the morning, and then halfway through the day you get pulled away to do something else.
"So, boards and ceilings are going up without asking the electricians or the plumbers if they've finished in the roof. They then have to cut out holes to bring their cables through."
INSIDE PONTIO
The worker also said tiles were expanding when water got into them and have been replaced several times due to the damage.
"It's just - it's a mess, to be honest."
He described the hurry to try to complete the building last September: "It was such a rush that the rest of the building was abandoned. I think the rush was so big, a lot of mistakes were done."
The worker added: "They might open in June. But you'll have some painters who'll still be there at least until September."
A spokesman for Middlesex-based Galliford Try said as with any project of the level of complexity that the Pontio building represents the construction team has faced "a number of challenges throughout the build programme".
He added: "None of these issues has been out of the ordinary experience of a construction process and all of these challenges are being met, ensuring that the high quality finish of the final building is not compromised.
"We remain committed to working collaboratively with the University of Bangor and all the stakeholders involved to reach a successful conclusion to this prestigious project as soon as is practically possible."
Bangor University said it is working with Galliford Try in order that they may complete the building "to a high standard of quality as quickly as possible".
A spokesman added: "Galliford Try have assured us that they will complete the building to a high standard of finish and we look forward to seeing the building open."
The Arts Council for Wales is currently withholding the final £1m of capital funds it has promised the project and has not given any capital funding since last July.
A spokesman said: "Although we are a minor contributor to the overall project costs, we have been very concerned about the well-publicised delays to this important project.
"We have urged Bangor University to work closely with the project contractors to bring outstanding matters to a speedy conclusion. The remaining funds that we have allocated to the project have been held back until that happens."
The Welsh government said: "We are keen that the current delays should not affect the longer term benefit of the project for the people of north Wales and will continue to support Bangor University so that the project can be completed as soon as possible."
A construction worker on the site of a new £49m arts centre in Gwynedd has described the project as "chaotic".