Some think the Church is the Kingdom of God. Although there is a connection between the two, they are not identical. Jesus Christ is the Head of the Church (Ephesians 1:22), which is the body of believers called by God to proclaim the coming Kingdom.
Christ rules His Church, thus it is under His sovereignty and royal power. We might say the Church is the precursor of the coming Kingdom of God. Or, to put it in terms that Jesus Christ used, we can say that the Kingdom of God is similar to the proverbial mustard seed, waiting for its germination and rapid growth at Jesus' return (Matthew 13:31-32).
The Bible, however, never uses the term "kingdom" to apply directly to the Church. Instead, it refers to God's prophesied world-ruling government.