We propose liquid-crystal-based reconfigurable chiral metasurface absorbers and numerically investigate their chiro-optical properties. The chiral metasurface absorber is based on a metal-insulator-metal structure on the substrate, which can strongly absorb a circularly polarized wave of one spin state and reflects that of the opposite spin, resulting a strong circular dichroism. A birefringent liquid crystal (LC) is exploited to serve as the insulator layer in the metal-insulator-metal structure. We could then vary the circular state of the incident light by controlling the alignment of the LC molecules, hence inversing the circular dichroism. The simulation results show that the sign of the circular dichroism can be effectively changed by externally controlling the alignment of the LC molecules in between the homogenous and homeotropic states. The absorption efficiency for the specific circularly polarized wave can be larger than 80% and the CD is nearly 70%. The simple and compact design of our proposed chiral metasurface absorber is especially favorable for integration, and such reconfigurable chiral metasurface absorber could find many potential applications in biological detection/sensing, polarimetric imaging, and optical communications.