The winning school will receive a visit from Blue Peter gardener Chris Collins, who will work with staff and pupils to recreate their winning design.
The competition opened this month and runs until 14 May.
Chris Collins explained: "This competition is a great way of sparking kids' imagination and getting them to think about gardening as a cool thing to do. It is open to individual pupils, groups of friends, the whole class or the entire school. I can't wait to see the all ideas people come up with and I'm really looking forward to working with the winning school to bring their ideas to life."
Pupils are asked to draw their designs on an A4 sheet of paper, write a short explanation and then ask their teacher to download an application form from www.puffinbookclub.co.uk.
The RHS has been working with schools through its Campaign for School Gardening since 2007, and in that time it has helped over 10,000 schools to start gardening.
By joining forces with the Puffin Book Club, the RHS hopes to encourage thousands more schools and students to get bitten by the gardening bug.
Subscribe to Horticulture Week for more news, more in-depth features and more technical and market info.