If approved, the centre could bring 120 new jobs, including both part-time and full-time positions, to the area.
Construction work could start by spring 2011 and the centre could open in the autumn.
Stuart Wright, director of property at Dobbies, said: "Our Serpentine Garden World will bring over 120 jobs to Peterborough and will encourage an environmentally-friendly approach to 21st century living where all the family can enjoy planting and growing.
"We want to help boost the local economy in a sustainable way by providing jobs for local people. We will also be working with Cambridgeshire suppliers to fill our Farm Food hall shelves, feature on the menu of our restaurant and provide the huge range of gardening and plant products."
Dobbies, who run 25 centres across the UK, say the new garden centre will be built on an 3.5ha site and try to be environmentally friendly with energy efficient lighting and a recycled water system.
Residents will be able to view Dobbies' plans for the site at Serpentine Green Shopping Centre in Hampton, Peterborough on 23 June from 2pm to 8pm.
Van Hage opened a new garden centre in Peterborough earlier this year as part of the £25m Peterborough Garden Park.
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