In this work, we proposed a state-of-the-art metasurface model that breaks the mirror symmetry and rotation symmetry of the structure. It consists of two-layer rotating gold split rings, and has the capability of chirality-selective absorption for circularly polarized light (CPL) in two bands. The absorption peaks for left- and right- circularly polarized (LCP&RCP) light appeared at 989 nm and 1404 nm, respectively, with the maximum absorptivity of 98.5% and 96.3%, respectively. By changing the rotation angle of the two-layer gold split rings, it could also be designed as a single-band chiral metasurface absorber, which only absorbed RCP light but not LCP light, and the absorptivity of RCP light could be up to 97.4%. Furthermore, we found our designed absorbers had the characteristics of great circular dichroism (CD) and symmetric absorption. The physical mechanism of the selective absorption of CPL by the absorbers may be explained by the current vector analysis. In addition, the absorption peak could be tuned with the changing of the geometrical parameters of the structure. The proposed chirality-selective metasurface absorbers could be used in CD spectral detection, optical communication, optical filtering, and other fields.