We propose a sound-absorbing nonplanar metasurface by considering locally different incidence angles along the metasurface. Perfect sound absorption is realized with the aid of hybrid resonance between two different subwavelength Helmhwoltz resonators comprising a unit cell. We theoretically investigate the effect of incidence angles on the sound absorption of the unit cells, and present a design method of the nonplanar metasurface that achieves perfect absorption by considering locally different incidence angles along the metasurface. The perfect absorption of plane sound waves on nonplanar surfaces is numerically demonstrated at the target frequency of 1 kHz. The numerical results show that at least 99.8% of the incident wave energy is absorbed by the designed metasurfaces with a thickness of λ/24. A nonplanar metasurface is fabricated via three-dimensional printing, and perfect sound absorption is experimentally validated at the target frequency of 1 kHz. Furthermore, we design nonplanar metasurfaces that can perfectly absorb cylindrical sound waves when a line source is located near the metasurface. While previous sound-absorbing metasurfaces focused only on planar surfaces, the proposed method achieves perfect sound absorption on nonplanar surfaces, expanding the range of practical applications in various industrial areas.