The development of new heterogeneous catalysts with stable catalytic activity in a wide pH range to prevent polluting precipitation plays a vital role in large-scale wastewater treatment. Here, a facile anion exchange strategy was designed to fabricate hollow CuS nanospheres by using CuO nanospheres as hard-templates. The structural and compositional transformation from CuO nanospheres to hollow CuS nanospheres were investigated via X-ray diffraction, scanning electron microscopy, transmission electron microscopy and X-ray photoelectron spectroscopy. The Fenton-like degradation of organic dyes was used to evaluate the catalytic performance of the obtained Cu-containing catalysts. Results reveal that the hollow CuS nanospheres have the best catalytic activity among five kinds of Cu-containing catalysts. Hollow CuS nanospheres can effectively accelerate the decomposition of HO into hydroxyl radicals and superoxide radical, which have been proven to be mainly oxidative species in the Fenton-like degradation of organic pollutants. Hollow CuS nanospheres have a wide pH application range of 5.0-9.0, and their extremely stable activity can be maintained in at least 15 catalytic cycles with a Cu ion leaching rate of less than 1.0 %. The outstanding catalytic performance of the CuS catalyst is expected to enhance the practical applications of copper sulfide catalysts in Fenton-like wastewater treatment.