A water pipe wrench structure consisting of a first wrench body and a second wrench body pin jointed by a control component. The first wrench body includes an actuating piece. A tooth space is positioned on this actuating piece. This actuating piece and a tooth piece extend with a uniform curvature. The second wrench body includes a perforation to pass the control component through this perforation and the tooth space. This control component includes a column piece and a grinding tooth piece, and the grinding tooth piece can be moved by pressure, so that the grinding tooth piece can be engaged to or separated from the tooth space and thus end the movement of the control component.