We investigate the Au(001) surface reconstruction, numerically, by Molecular Dynamics (MD) simulation. We find that the top-most layer of Au(001) surface is reconstructed to a contracted hexagonal face, and relaxed about 0.05$AA$ upward at room temperature. The contraction ratio with respect to a unreconstructed Au(111) surface is about 3.5%. The hexagonal layer is slightly distorted and buckled. The surface corrugation is found to be about 0.28$AA$ on average. In our earlier work we have predicted the in-plane orientation of the reconsturcted layer to be either $0^{circ}$ or $0.7^{circ}$ depending on the size of the cluster. However, we find only $0.0^{circ}$ in this simulation because the size of the cluster correspoding to the $0.7^{circ}$ orientation is larger than the current limitation of MD simulation. These findings are in good agreement with experimental results.