It seems like an odd question. God just IS. But I'll take a stab at an answer. God is life and the source of all life, so that could be a purpose, I guess. God is truth and the source of all truth, so that could be one, too. God maintains and sustains the universe. God has a purpose to reveal Himself so that we can be in relationship with Him. God has a purpose of redeeming as much of humanity as will let Him.
I made a list once of what God is probably doing any given day. Maybe this will address your question as well.
- He sustains all of creation (Heb. 1.3)
- He holds all of creation together (Col. 1.17)
- He upholds the cause of the oppressed and gives food to the hungry. The Lord sets prisoners free (Ps. 146.7)
- He is continually working to reconcile all things to Himself (2 Cor. 5.19)
- He is continually working to draw all people towards Him (John 12.32)
- He is reconciling people to Himself (2 Cor. 5.18)
- He gives appropriate spiritual gifts to people (1 Cor. 12-14)
- He indwells His people and His Church (Eph. 2.22)
- He listens to and answers prayers (many, many many references)
- He is seeing His plan of salvation through to its conclusion.
- He is revealing Himself through His creation and to His creation.