Plan a trip with your parents. manage everything alone. show your parents your capacity to handle such thing. then convince them with your passion. just remember nothing is impossible. do not reverberate yourself for the fear of rejection. best wishes for you.
You can make this excuse that this is the last tour from our office and we will not get this chance again in my life as everyone don't get a chance to go on a trip after marriage all my freedom will come to an end.
It means you have not shown them enough reason to trust you for travelling....start acting up..parents know if their kid is ready or not for doing certain things.If your situation is different then apologises beforehand.
It is not clear from your query that whether they don't let you travel alone or they don't accept your travelling as your profession. So there may be different reasons. Firstly they might be afraid of your travelling all alone. So for that you to manage another person so that he or she can accompany you in your journey. Doing this it might make your parents feel secure. If you want to take travelling as your profession, you need to convince your parents about how you are going to make money though it. You could also start your own travel agency. Doing this it will let your parents support you in following your passion. Happy travelling!