A symmetrically breaking nanostructure, equilateral triangle with triangle notch, is designed. The extinction spectrum and surface electric field distribution on the structure surface are investigated by the discrete dipole approximation method. The results show that a Fano resonance line-shape occurs in the extinction spectrum, which results from the interference between the bonding and antibonding hybridized plasmon resonance. The effects of the structural parameters of the symmetrically breaking nanostructure on resonance mode are also studied.