How can I remove my hesitation for speech in front of public?

Glossophobia or speech anxiety is the fear of public speaking or of speaking in general.
The word glossophobia comes from the Greek 'glōssa', meaning
tongue, and phobos, fear or dread.

By practicing speaking in front of an audience small in number made up of people who are known to you.Consistent practice is the key. I would recommend you to be a part of the Toastmasters club (google them to know more) and be a part of your nearest toastmasters club.
Apart from the conventional methods like improving your vocabulary and practicing with audience as well as in front of the mirror, I suggest you to start regularly visualizing yourself in front of a crowd giving a speech at the peak of your confidence. Make that picture as vivid and as clear as possible. Also visualize a positive audience reaction to you. Doing such a creative visualization will help your brain to rewire itself and that will be of immense help in getting you out of public speaking fear.

Finally, know that no one is perfect and even if you make mistakes people will forget them by late evening. But think of it on the lines of how regretful you will eventually become (may be in a few months or years) if you do not 'Talk' your thoughts out loud to people, today. What if your speech contains the message that most of them need to hear?

THINK!!!