A left-handed material composed of unit cells of three-layered square nanoflake with four edges gapped is proposed in this paper. The S-parameters of the unit cell are caculated in the numeric simulation, and the property parameters such as the retrieved complex refractive index n, permittivity ε and permeability μ,etc. are analyzed. It is shown that, the frequency band in which the refractive index of this structure being negative lies from blue in the visible region to near ultraviolet, and the peak of negative refractive index lies at 748 THz, namely the violet end of the visible region. And the figure of merit of the material is 154, so it may have practical applications because of its low loss and high transmission.