Involve your parents in the planning and preparation of your trip. Ask for their advice and include them in the project. Parents absolutely love the idea of being indispensable.
What kind of work will you apply for? Do you want to save up money from home or work during your trip? Parents who sense that their children are showing some initiative themselves feel much more inclined to reach out for their wallet and help out financially.
Aim for frequent communication with your parents by SMS, email/Skype and/or phone. You can also set up a travel blog or (if your parents are very old school) send letters. Make a flexible "plan" - in that way you'll avoid worrying your parents too much if you miss a "deadline" now and then. And remember, close contact is the primary source of peace of mind in the universe of parents.
Give a copy of all travel documents to your parents so that they'll always be able to follow your route. Remember also to scan/copy your most important papers - passport, tickets, visa etc. - and keep them with your parents. If you lose all your valuables, they'll still have the "evidence". First of all, it's always a good idea to keep a backup of all your documents, and secondly, your parents will get the feeling that they play an important and protective role for your well-being. To protect and serve - their offspring, that's what parents are all about. And while you're at it, also remember to keep copies of your documents in your email or on your USB stick/phone etc.
KILROY travels has many years of experience (fact) in sending young people, such as yourself, on backpacker trips and round the world journeys. We specialize in offering you and your globetrotter friends the absolutely best service, best offers and best security possible all over the world. If your parents are worried or just plain curious, then invite them over to meet your travel consultant and we will do our best to explain the situation and put them at ease.
If none of the above helps you can always start pestering your parentsuntil they give in to your wishes. It has worked before and it will probably work again!