A sucker assembly includes a sucker, a pull bar secured on the sucker, a pressing member mounted on the pull bar and pressing the sucker, an elastic member mounted on the pull bar and biased between the sucker and the pressing member, a control handle pivotally mounted on the pressing member, and a pivot shaft extending through the control handle, the pressing member and the pull bar. The pressing member has a periphery provided with a mounting seat which has a fixing recess to receive a hanging rod of a support rack and to abut a surface. Thus, the hanging rod of the support rack is locked onto the surface by the fixing recess of the mounting seat so that the support rack contacts with the surface exactly and closely.