The Pope in Rome was always considered to be the head of the Catholic Church since its founding. Some Biblical evidence of this (Peter being the first pope) from the Catholic interpretation follows:

Jn 20:6 - Peter, despite arriving at the tomb second, was permitted in Jesus' tomb first.

Acts 2:14-36 - Peter is the first to spread the gospel.

Acts 5:15 - Peter shown in extremely high regard by Christians

Acts 15:7-11 - Peter presides over an ecumenical council. After he speaks - everyone else shuts up and what he said goes despite some disagreement.

Peter's name appears more than double the amount of any other disciple in Biblical texts.

(Make sure you are using a Catholic approved Bible when examining these verses, such as the New American Bible)

There is also an impressive amount of texts from the Church fathers concerning these issues if you are interested. I will gladly provide some sources.