Blue phases (BPs) are expected to be applied to new liquid crystal (LC) materials because they are optically isotropic upon no electric field and show high speed response to an applied electric field. Since BPs appear when chirality of molecules is enough high, the chiral dopants which are added to nematic LC to induce a BP are required to have large helical twisting power (HTP). On the other hand, fluorinated nematic LCs are generally used for the LCD because they can prevent from containing polar impurities in the LCs and show low viscosity. In this study, we designed the novel fluorine substituted chiral dopants which are expected to have the characteristics similar to fluorinated nematic LCs and indicate high HTP by using a binaphthyl skeleton. We will discuss relationships between the structures and HTP of chiral dopants in chiral nematic phases and electro-optical properties in BPs.