Anomalous reflection from metasurfaces with 100% efficiency at optical frequencies was not achieved until an all-dielectric quasi-three-dimensional subwavelength structure was proposed. The desired nonlocal control of light waves is realized by designing phase responses of multilayer films at a single wavelength. However, a high-efficiency bandwidth is not controllable by designing only the phase response at a single wavelength. Here, we propose the use of a multilayer metasurface to achieve anomalous reflection with a customized high-efficiency bandwidth. The interference of the successive light waves scattered from the structure at multiple wavelengths is controlled by phase dispersion regulation of multilayer films. As a proof of concept, two sets of multilayer films with different phase dispersions were designed to realize broadband (∼110 nm) and narrowband (∼15 nm) anomalous reflections, both with an efficiency of over 80%. The results offer a general strategy to design high-efficiency anomalous reflection with arbitrary bandwidth and might stimulate various potential applications for metadevices.