Certainly He was fully human, but He was also fully God. Jesus couldnt have delivered us from the fear of death if he was himself afraid of it.
What Jesus felt was dread, Dread of separation from His Father. He'd never experienced that before. He was always one with him. When Jesus became sin, God could not behold His son anymore because He is too holy to look upon sin. And then on the cross Jesus cried out "Fathe, Father", why have thou forsaken me?"
We know from John`s gospel that Jesus sweat drops of blood in the Garden of Gethsemane before His death, and said: "Abba, Father, all things are possible to you. Please remove this cup from me. However, not what I desire, but what you desire." A man who felt fear would have begged the Father to spare Him. Jesus did not. He expressed dread of that task before Him, yet He stated clearly, "Your will, not Mine."