Plasmonic nanosensors have emerged as a powerful tool for biosensing and other applications. Therefore, efforts are underway to achieve higher sensitivity for these nanosensors. In line with this goal, we have investigated the sensitivity of silver square and triangular chiral nanosensors based on two strategies, Localized Surface Plasmon Resonance (LSPR)-based and Circular Dichroism (CD)-based sensing. Chiral nanostructure parameters (height, diameter) and the angle of incidence light have been optimized with calculation method (3-D finitedifference time-domain (3-D-FDTD)) in order to obtain best localized surface plasmon resonance and consequently the highest sensitivity. The calculation results show that sensitivitys~1727 and 1658nmRIU -1 can be achieved in LSPR-and CD-based sensing method respectively for square chiral nanostructure, which are significantly more than previous works.