Try to think it differently.
You are probably actually thinking that they will judge you. Think that you are not there to be judged but that you are about to give pleasure to the listeners.
They are here to listen to you, share something with the listeners.
Also, take your time before playing, take deep breaths, think about something related to what you're going to play to enter an environment in relation to what you're about to play or play for someone, and only once you feel ready, GO!

When I play in public I take about 30seconds after I've sit and before I start playing. This is very important, it's concentration.
You can take more time if you need, remember that music comes from silence ( and ends by silence)
This post was edited by unid_element59 on Sep 22 2011 01:51pm