The elasto-plastic deformation behavior, yield strength and strain rate of material under shock compression can be represented by shock front, and the shock front is also related to the variation of strength after shock compression. In this paper, we study the dynamic plastic deformation processe of nanocrystalline copper under shock compression through molecular dynamics simulations. We also explore the dependences of the shock front and the mechanism of elasto-plastic deformation on grain boundary, and make a comparison with the case of the shock response of nanocrystalline aluminum. This investigation shows that the contribution of grain boundary to the shock-front width of nanocrystalline copper are smaller than that of nanocrystalline aluminum. The plastic mechanism of nanocrystalline copper is dominated by the emission and propagation of partial dislocations, and the full dislocation and deformation twin are rarely found in the samples. From the simulations are also found that the shock-front width decreases with the increase of loaded shock stress. A quantitative inverse relationship between the shock wave front width and the shock intensity is obtained. This quantitative inverse relationship is close to other simulation result of nanocrystalline copper and quite different from results of coarse-grained copper compression experiments.