A new two-dimensional left-handed material based on double-triangled sructure is proposed. The simulation software HFSS is used to analyse the structure and its derivative structure. Results show that this type of structure can present left-handed properties when electromagnetic waves are incident on either perpendicularly or parallelly the plane of the substrate. And the general rule for this type structure is that: When the incident electromagnetic wave is in the perpendicular or parallel direction, and for each additional metal strip in the middle of the metal wires, the resonant frequency of the structure moves to higher frequencies around 0.5 or 4 GHz. These can be of reference values in further development of multi-dimensional left-handed material.