The charity is also raising funds to create more horticultural apprentice positions over the next five years at its four gardens: RHS Garden Wisley in Surrey, RHS Garden Harlow Carr in North Yorkshire, RHS Garden Hyde Hall in Essex and RHS Garden Rosemoor in Devon.
RHS director general Sue Biggs said: "Horticulture is a vibrant, challenging and diverse industry with great job prospects...However, research over the last few years for the industry-wide Horticulture Matters campaign has found that 70 per cent of 18-year-olds believe that horticultural careers should only be considered by people who have ‘failed academically'.
"We also know that more than 80 per cent of secondary school teachers who discussed careers with their pupils said that they themselves were not aware of the vast opportunities offered by a career in horticulture."
Visitors to Chelsea will be able to make a donation to receive an RHS Chelsea Appeal 2014 badge.
Fashion designer Paul Smith and TV stars Piers Morgan and Laurence Llewelyn-Bowen have joined a collection of other RHS supporters to create drawings of gardens, which will be auctioned off on eBay during RHS Chelsea Flower Show week to raise funds for the appeal.