A floating fastener mounting structure includes a mounting socket having an annular bottom stop flange and mounting portion extending around a bottom end of a center hole thereof, a locking member including a shank inserted through center hole, a mounting head located at the top end of shank and suspending above center hole and an expanded locking end tip located at the bottom end of shank and movable in and out of the bottom end of center hole, a spring member mounted around shank and stopped between mounting socket and locking member, a cap member fastened to mounting head and having an outer diameter not larger than outer diameter of annular bottom stop flange and defining an accommodation chamber for accommodating a part of the mounting socket and a part of the mounting head. The mounting portion is downwardly inserted into a mounting through hole, and then a stamping process is applied to deform the peripheral wall of mounting through hole into a riveting portion and to simultaneously force riveting portion into engagement with the mounting portion tightly.