A double band left-handed (LH) microstrip is designed based on defected ground structure (DGS) and Split Ring Resonators (SRRs) with broad bandwidth and low loss while the size of the unit cell is small and the synthesis is simple. Its effective permittivity and permeability are both extracted from the transmission and reflection data of the left-Handed microstrip, then the wave number k is calculated, and the results demonstrate that the LH microstrip shows backward wave (BW) properties in the broad frequency range of interest.