We present a new realization of weak electrostatic force based on Kelvin capacitor, which, compared with the conventional realization, simplifies the mechanical design without synchronously moving the central and guard-ring electrodes. However, a residual force due to the edge effect of the capacitor should be accurately known. In this paper, an analytic model of the electrostatic force generated from the edge effect is presented based on conformal transformations. The accuracy of the model is verified by the finite element calculation based on a micro-Newton weak force generation.