I have many fears:
A fear of drowning.
A fear of falling.
A fear of heights.
I also have a fear of sharing the Gospel with people one-on-one and handing out Gospel tracts!
There's something about not knowing what the person's reaction will be that makes sharing the Gospel a frightening thing.
And what makes this fear worse than any other fear is that it is spiritual in nature, and Satan and his demons exploit it to the utmost! If they can discourage someone from sharing about Christ, they will!
It's important to pray and not go out in our own strength, but rely on the strength of God!
Something else I hope will help you when you think to share the Gospel with someone and feel afraid: think of the persecuted Church!
Think of all that they give up for the privilege of sharing the Gospel with their neighbors:
Determine that it is an honor to stand with these faithful ones, even if you do not face the same hardships they do. Determine in your heart to take a stand for Jesus Christ, because many will stand for him even in the face of imprisonment and death!
Be proud to stand with them!