We study dual-Fano resonances and its sensing properties in a crossed ring-shaped metasurface by use of the finite-different time-domain (FDTD) simulation. The results show that the dual-Fano resonances in the proposed crossed ring-shaped metasurface are caused by the interaction among three local surface plasmon resonances (LSPRs), and the spectra of dual-Fano resonances can be tuned by the radius of the circular ring (CR) nanostructure, the distance between the center of the two CRs in x direction, and the polarization of the incident light. Interestingly, single Fano resonance splits into dual-Fano resonances in the case of asymmetric ring structure arrangement or non-y-axis polarized incident or the distance d<120 nm. Moreover, we can also find that the refractive sensitivity in the proposed crossed ring-shaped metasurface can reach up to 1010 nm/RIU and 1300 nm/RIU at Fano resonance peak 1 and Fano resonance peak 2, respectively. These results may play an important role for designing high sensitive plasmonic sensors.