Initial stage of nano-void growth in single crystal copper under shock loading along direction has been investigated by using molecular dynamics (MD) simulation. The results show the void growth rate, represented by iucrease of equivalent radius of void vs time, keeps constant under certain shock strength. Two kinds of dislocation mechanisms of single void growth have been observed. When shock strength is lower than a critical value, dislocations nucleate and move outward only in the area around two vertices of the void along the shock direction and the void only grows along shock direction. When shock strength exceeds the critical value, dislocations nucleate and move outward not just in the above area but also in the equator perpendicular to the shock direction, and the void grows both along the shock direction and its normal. By examining the displacement history of atoms around the void surface, we find that the radial velocities of the vertices along and perpendicular to the shock direction almost keep constant during the tensile process. Based on constant radial velocities of vertices, we have derived a model of void growth which explains the constant void growth rate well.