To provide a connection structure of flanged pipes capable of maintaining satisfactory sealing property without retightening them and improving its assembly workability.

In this connection structure of the flanged pipes 1, 2, a first flange part 1B is provided with a first seal end part t1, a second flange part 2B is provided with a second seal end part t2, an annular channel 6 is formed on an outside diameter side of a fluid passage 4 in the first seal end part t1, an annular projection 8 press-fitted into the annular channel 6 is formed on an outside diameter side of a fluid passage 4 in the second seal end part t2, and a drawing-close means M for drawing the first and second flange parts 1B, 2B close for each other and maintaining its drawing-close condition is provided. The annular channel 6 in the first flange part 1B and the annular projection 8 in the second flange part 2B are mutually fitted to form a fitting seal part 3.