Thank you for writing. Fear of failure can be a serious hindrance to our Christian life. But as with all problems, the Lord has given help for us through His word.
I am a little confused about your first statement. You say that you "became a believer because of the fear of failure." Perhaps it was your fear of failure that made you look for help and your search for help ended up leading you to Jesus Christ. God has used many things to bring us to Himself. However, if you think that becoming a believer in Jesus will keep you from ever failing in anything, you have come for the wrong reasons and will not get what you seek. I will assume that you have truly believed in Christ for the sake of this advice. I only ask you to examine your heart to make sure of your salvation.
Knowing Christ does not mean that we will never fail, but it does mean that we do not need to live in fear. 2Timothy 1:7 states, "For God hath not given us the spirit of fear; but of power, and of love, and of a sound mind." The spirit of constant fear in the believer is not from the Lord. "There is no fear in love; but perfect love casteth out fear: because fear hath torment. He that feareth is not made perfect in love" (1John 4:18). There is something called the fear of the Lord, but the fear of failure is not the fear of the Lord. It is a human fear, like the fear of man. Proverbs 29:25 states, "The fear of man bringeth a snare: but whoso putteth his trust in the LORD shall be safe."
Fear is the opposite of faith. We fear because we do not have complete faith in God. The way to overcome our fear is to increase our faith. Faith is a fruit of the Spirit (Galatians 5:22-23), so we must walk in the Spirit to have faith. It comes by the word of God (Romans 10:17), so we must seek help from the Bible. It comes by prayer (Matthew 17:20-21), so we must go to the Lord in prayer in order to increase our faith.
Fear of failure comes because we have tied our worth to external success. We may feel that others require it of us. We may have set the standard for ourselves. However, we have not fully surrendered all we do and all our results to the Lord. Paul set high goals for reaching the lost and establishing churches. But he also understood that the fulfilling of those goals depended entirely on the Lord. To the Corinthians, he said (1 Corinthians 3:6), "I have planted, Apollos watered; but God gave the increase." He gave God all the credit for giving the increase.
Perhaps a personal experience would help at this point. For several years when I first became pastor of our church, it struggled. I felt like a total failure in the work that God had called me to do. Finally, at a time of crisis in my heart, I told the Lord that I was willing to be a failure for Him if that was what He wanted for my life. It did not matter what I did or became. It only mattered that I was obedient to Him and was willing to be used of Him as He saw fit. That day, God gave me a special peace. In fact, He has blessed in many ways since that time.
I encourage you to turn your life over to the Lord no matter what the external results. He will take care of you--even if you go through times that seem to be failure. We must come to the point where we are even willing to fail for God. May the Lord bless you.