In the present paper, micro-scale contact induced by liquid bridging is studied numerically via FEM with consideration of coupling effect between the liquid bridging and the elastic deformation of the half space. The variations of the liquid-bridging force and contact area as functions of a dimensionless parameter χ (measurement of relative stiffness of the contact bodies) and the filling angle ψ (measurement of liquid volume) are obtained and discussed. The FEM numerical solution is compared with two approximate analytical solutions based on Hertzian contact mechanics. It is found that the dimensionless liquid bridging force and contact area obtained via the approximate solutions are much smaller than the values obtained via FEM under certain conditions. The error inhabited in the approximate solution is due to the coupling effect between the liquid-bridging force and the elastic deformation of the half space.