"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." (1 John 4: 18)
Many believers who learn about the grace and truth of Christ in them will still feel fear in their lives.
Does that mean that Christ's love is not perfect? Not at all, for the previous verse could not be clearer on this matter:
"Herein is our love made perfect, that we may have boldness in the day of judgment: because as he is, so are we in this world." (1 John 4: 17)
A better translation indicates that this love does not originate with us, but rather for us:
"Herein is love made perfect with us, that we may have boldness in the day of judgment; because as he is, even so are we in this world." (1 John 4: 17, ASV)
Furthermore, the initial verse carries with it an intensive, progressive element in "fear":
"fear is not in the love, but the perfect love doth cast out the fear, because the fear hath punishment, and he who is fearing hath not been made perfect in the love;" (1 John 4: 17)
John speaks to a man who actively lives in fear, or "is fearing".
Also, to the extent that we sense fear about anything, to that extent God's love has not yet invaded in some part of our lives.
Are you afraid of losing your job? See Jesus as greater than your boss, your deadlines, as the one who lives and works in you and through and all throughout your circumstances, trusting that all things work together for good (Romans 8: 28)
Are you afraid of losing a loved one? See Jesus' perfect love for you, a love which was in place for your before the world began:
"22And the glory which thou gavest me I have given them; that they may be one, even as we are one: 23I in them, and thou in me, that they may be made perfect in one; and that the world may know that thou hast sent me, and hast loved them, as thou hast loved me. 24Father, I will that they also, whom thou hast given me, be with me where I am; that they may behold my glory, which thou hast given me: for thou lovedst me before the foundation of the world." (John 17: 22-24)
God loves us as much as He loves Jesus. This is a love which we need to learn more about! In fact, Paul prayed that we would all have this revelation:
"14For this cause I bow my knees unto the Father of our Lord Jesus Christ, 15Of whom the whole family in heaven and earth is named, 16That he would grant you, according to the riches of his glory, to be strengthened with might by his Spirit in the inner man; 17That Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love, 18May be able to comprehend with all saints what is the breadth, and length, and depth, and height; 19And to know the love of Christ, which passeth knowledge, that ye might be filled with all the fulness of God." (Ephesians 3: 14-19)
So, any fear we have in our lives is cast out as we comprehend more of God's love for us through Christ.