Large-scale molecular dynamics simulations are performed to study the adhesive contact between a rigid spherical tip and an elastic flat substrate. We focus on he relations between the real contact area and the external load and between the repulsive force and attractive force on contact interface. The simulated results are consistent with the corresponding continuum contact theories, which are Hertz model, Ggeenwood-Williamson (or Persson) model and Maugis-Dugdale model according to surface roughness and interfacial adhesion. We show that there are same relations between the real contact area and the repulsive force for both non-adhesive and adhesive contact, which means that the effect of adhesion on contact behavior can be equivalent to that of a virtual load. We demonstrate that the attractive force on contact interface increases with the real contact area in a power-law function, with a power exponent larger than 1 for the atomic-scale smooth tip and with a power exponent smaller than 1 for the atomic-scale rough tip.