In this study, the design and analysis of a butterfly valve disk was performed to minimize the rubbing between the disk and the seat at opening and closing. The butterfly valve has double eccentric structure and the contact surface between the disk and the seat is a conical surface. At the instant of opening and closing the valve by the rotation of disk, the positions of zero contact point are changed. Also, if the cone surface is cut in the perpendicular direction to the rotation axis of the valve, the contour of cutting section is hyperbolic. Therefore minimum distance between the origin of the eccentric axis and the hyperbolic curve goes to the position of zero contact point. In order to consider the interferences between the disk and the seat, the thermal-structure coupled field analysis was performed by ANSYS.