Controlling the formation of the conductive network in the polymer nanocomposites (PNCs) is very meaningful to enhance their electrical property.In this work,we investigated the effect of grafted nanoparticles (NPs) on the conductive probability of PNCs in the quiescent state as well as under the shear field via a coarse-grained molecular dynamics simulation.It is found that the smallest percolation threshold is realized at the moderate grafting density,the moderate length of grafted chains or the moderate interaction between grafted chains and free chains.Corresponding to it,the dispersion state of NPs varies from the contact aggregation to the uniform dispersion.By analyzing the connection mode among NPs,the probability of NPs which connect three other ones reaches the maximum value at their moderate dispersion state which is responsible for the optimal conductive probability.In addition,the main cluster size is characterized to better understand the conductive network which is consistent with the percolation threshold.It is interesting to find that the percolation threshold is smaller under the shear field than under the quiescent state.The shear field induces more NPs which connect three other ones.This benefits the formation of the new conductive network.Meanwhile,the anisotropy of the conductive probability is reduced with increasing the grafting density.In summary,this work provides a clear picture on how the conductive network of grafted NPs evolves under the shear field.