A new 2D left-handed material structural unit is proposed by setting two reversely symmetrical Z metal strips on each side of the dielectric substrate respectively. The structure can present left-handed properties in X waveband, with electromagnetic waves incident either perpendicularly or parallel to the plane of the substrate. By means of numerical simulation, extracting the effective permittivity and permeability from S parameters and building the equivalent magnetic resonance circuits of the structure, the left-handed property is further analyzed and verified. And by comparing the double Z-shape unit with the traditional H-shape unit, it is shown that they have similar responses of presenting left-handed pass band when electromagnetic waves are incident perpendicularly to the substrate, but only the double Z-shape unit can achieve left-handed features when electromagnetic waves are incident parallel to the substrate. The results indicate that the double Z-shape left-handed structural unit is superior to the traditional H-shape structure, namely, the double Z-shape can redound to design left-handed structural unit for double dimension incidence of electromagnetic waves.