The story of the Tower of Babel is found in the Book of Genesis, Chapter 11. In this chapter, we are told that after the Great Flood, all of humanity spoke the same language. They decided to build a tower that would reach all the way to heaven, so that they could make a name for themselves and never be scattered.
However, God was not pleased with their plans. He came down and confused their language, so that they could no longer understand each other. This caused them to abandon the tower and scatter throughout the earth.
So, we can conclude that the Tower of Babel was built after the Great Flood.