The Apostle John wrote his first letter to the Churches of Asia Minor, in which he expressed: "God is light", "God is love". The letter begins with an exhortation to live in the light (1 John 1: 5), to not love the world (1 John 2:15), to follow the fraternal love (1 John 3:11), ending with a request to live in the love of God, expressing: There is no fear in love. But perfect love drives out fear, because fear has to do with punishment. 1 John 4:18.
What does perfect love mean to the Apostle? A perfect virtue is a virtue that can not be surpassed in its genre. In the gender of love, perfect love is the love projected towards the whole creation of God, God loves his work, this is known as Love of Charity or Agape.
The Apostle affirms that this type of love eliminates fear, because fear implies punishment. Speak of punishment is speak about the sin. It is proper for the sinners to "feel" a diffuse fear, sin implies a punishment: you reap what you sow, thence the fear. For the people who live the Charity, sin is not an habit but the exception. This is why the Charity eliminates fear, those who not practice the sin does not have to fear.
Let's see this from the perspective of God:
To understand the relationship between the perfect love and the fear, we must understand what passions can be in God. Can be feel fear God? God in his omnipotence can not be afraid of his creatures, fear does not exist in God, also hate. Who is not afraid can not hate. Fear is the result of the concupiscence, not of the friendship with God, who sins, feel fear, because sin is related with punishment either divine or product of what around us, "You reap what you sow".
Those who are worthy of divine love can not feel these negative emotions. Fear, anger, shame, guilty are passions that guide man to evil. In another sense you could say that the unicity of God demands that passions are absent in God, passions reveal the existence of a "division of the mind", remember that passions have their own desire regardless of the reason. This does not happen with the attachments, such as joy and hope, attachments perfect and strength the will. Recall that we can only attribute to God the perfections that we see in the creation, passions as fear can only be attribute to God metaphorically.