According to Christian belief, Jesus Christ's father is God. Christians believe in the doctrine of the Holy Trinity, which teaches that God exists as three persons in one: God the Father, God the Son (Jesus Christ), and God the Holy Spirit.
In this belief system, Jesus is considered the Son of God, and his conception is described as the "Virgin Birth," where the Holy Spirit overshadowed Mary, and she miraculously conceived Jesus while remaining a virgin.
So, while Joseph was Jesus' earthly, legal father (as he was married to Mary), Christians believe that Jesus' true father is God, as part of the Holy Trinity.