A broadband ultrathin sound absorption or sound insulation structure controlling an acoustic wave propagation path has at least one sound absorption unit or one sound insulation unit; and each sound absorption unit or sound insulation unit has at least one acoustic wave focused section and at least one acoustic wave absorption section. The acoustic wave focused section is formed by an acoustic wave focused cavity filled with acoustic material. The acoustic wave focused section controls the acoustic wave propagation path through the change of a section of the cavity and the change of material equivalent parameters in the cavity, so that the acoustic waves are focused and propagate along the curve. The acoustic wave absorption section realizes efficient broadband sound absorption through the filled sound absorption materials and the arranged periodic local oscillators along an ultralong path of acoustic wave absorption labyrinth passage.