If approved the move would create 50 new jobs.
Plans include an extension of its indoor retail space, and add a larger café by extending the building to the east and south.
A canopy above the sales area for plants would be enlarged and car parking spaces will be reduced from 266 to 242 to increase space for landscaping and allow installation of a pedestrian access point next to the existing crossing island on the A59.
Poppleton Garden Centre also hopes to use land at the back of the centre to grow more stock.
The extension would partly replace a number of extensions, sheds, and metal containers, and provide an additional 1,553 sq metres of floor space.