Negative permittivity can be realized from the periodic unit cells of the metallic bar structure. Two-dimensional left-handed material based on metal-rod pair structure is proposed. Propagation characteristics of two-dimensional left-handed material are studied by the time-domain finite integration method. Simulation shows that the structure has good left-handed property at the frequency of about 0.76 THz. Results indicate that this construction exhibits negative equivalent permittivity and permeability simultaneously in 0.75~0.78 THz, and the double negative pass band is 0.03 THz. Double negative pass band changing with structural parameter of metallic rod pairs is studied, indicating that it is related with the space between metallic rod pair, length and substrate thickness. The results provide a certain reference to design and study of left-handed material in terahertz range.