The chain has submitted a planning application to Ards and North Down Borough Council and is targeting an early 2018 opening date.
The planned development is in partnership with the Magherafelt-based Conway Group.
It has worked on other Premier Inn developments in Lisburn and Londonderry.
Premier Inn is the UK's biggest hotel brand with more than 700 hotels across the UK and seven in Northern Ireland.
The firm's acquisitions manager Matt Aubrey said they had been looking for a suitable site in Bangor for a number of years.
He added that the development would represent an investment of Â£7m.
Conway Group is also planning to build 14 apartments on part of the site at Castle Park Avenue.
Premier Inn is planning to open an 85-bedroom hotel in Bangor on the site of the town's old leisure centre.