A non-aqueous liquid electrolyte for a secondary battery, containing an electrolyte, and at least one or more cyclopropane compound selected from the group consisting of a compound represented by the following formula (I-1), a compound represented by the following formula (II-1), and a compound represented by the following formula (III-1) in an organic solvent, wherein R11 to R15, R21 to R24 and R31 to R34 represent a hydrogen or a specific substituent; L11, L21, L31 and L32 represent a specific linking group; X represents an electron-withdrawing group; and n and m each independently represent 1 or 2.