Conquering fear is not an easy thing. That is why we see courage as a desirable trait. A sense of security develops courage in us. We can face fear because we are secure in God's love for us. I John 4:16-19 tells of God's perfect love and how it conquers fear.
"So we have come to know and to believe the love that God has for us. God is love, and whoever abides in love abides in God, and God abides in him. By this is love perfected with us, so that we may have confidence for the day of judgment, because as he is so also are we in this world. There is no fear in love, but perfect love casts out fear. For fear has to do with punishment, and whoever fears has not been perfected in love. We love because he first loved us."