I don't think it is possible to eliminate all feelings of fear. The question is what we do when the feeling of fear happens. When Jesus was talking about how we cannot work for God and money at the same time without cheating on one or the other, he recognized that this teaching would cause some fear in people. He noted that we would worry about what to eat or what to drink or where we'd get clothing, but he said we should not let this kind of fear stop us from stepping out in faith. He referring to the people who indulge these fears as "ye of little faith", thus showing that our choice will be for fear, or for faith. One will lead us away from the other.
There is always a reason why we feel fearful. Sometimes that reason is hidden from us, either because we're just been lazy about self examination, or because we do not want to confront the source of that fear. When you start to feel fearful, it is important to think carefully as to why you feel fearful. It is not enough to just say, "I don't know why". There is a reason, and you need to examine yourself until you find that reason. Ask God to help you see what you might not want to see; if you are sincere, he will help you to see it.
His rod and staff comfort me.
