Abstract: A faucet connecting structure contains a body including a chamber having a receiving trench, the receiving trench including an opening; an outlet pipe including a first end to input water and a second end to output water, the first end including a connector inserted into the receiving trench; an engaging member including a peripheral fringe, an inner surface, an outer surface, a first and a second segments, a slot, and the inner and the outer surfaces including at least one first deformable area and at least one second deformable area respectively to generate a radial-direction deformation when being forced in a radial direction so as to act against a radial-direction engaging force resulting from connecting the first engaging member and body together; a retaining means to retain the engaging member and the body together so that the outlet pipe is limited to move and rotate axially relative to the body.