The verification and calculation of the negative refractive index of a meta-material is carried out by the finite difference time-domain method. A slab and a prism of the meta-material are simulated. A genuine plane wave is generated by a two-direction periodic boundary condition (PBC) in the slab model Based on an advanced phase extraction technique, the negative refractive index of the meta-material is verified by phase velocity measurement in the slab and prism measurement. From our results, not only the phenomenon of backward phase propagation but also the negative refraction is clearly observed. The index is also calculated precisely. The results from the two models are consistent.