Monolithic nanoporous copper (NPC) ribbons with bimodal channel size distributions can be fabricated through chemical dealloying of Mg-32 Cu alloy in an acidic solution at room temperature. The microstructure of the as- dealloyed samples was characterized by X-ray diffraction, scanning electron microscopy, and energy dispersive X-ray analysis. These NPC ribbons are composed of interconnected large-sized channels (hundreds of nm) with highly porous channel walls (tens of nm). Both large- and small-sized channels are open, bicontinuous, and interpenetrating. Additionally, it is the first time to find that the evolution process of porous structure along the thickness direction of samples during the dealloying is from the interior to exterior, which is just contrary to the coarsening process along the thickness direction during the post-dealloying. Meanwhile, the corresponding mechanism is discussed in detail.