Recent research has revealed that some grain boundaries (GBs) can migrate coupled to applied shear stress. In this paper, molecular dynamics (MD) simulations were performed on sixteen [0 0 1] symmetric tilt GBs of bicrystal Cu to identify atomic-scale GB migration mechanisms and investigate their dependence on GB structure. The misorientation angles (θ) of the sixteen GBs cover the interval from 0° to 90° and a wide range of Σ values. A general method was proposed to explore the possible GB structures for each misorientation angle. Molecular statics simulation at a temperature of 0K were carried out first to determine the equilibrium and some possible metastable structures of the sixteen investigated [0 0 1] GBs. MD simulations were then conducted on the bicrystal models at equilibrium by applying a shear strain parallel to the GB plane. Shear deformation caused the tangential translation of the grain and induced normal motion of the GBs. This boundary coupling motion was present in the entire range of misorientation angles. Different mechanisms of coupled boundary motion at atomic scale were carefully examined in this work. The common feature of these mechanisms can be regarded as the displacement of local atoms and rotation of certain structure unit. Structure phase transformation of GB was found during the migration of Σ17(4 1 0) and Σ73 (8 3 0) GBs.