In this study, we derive an analytical model of an electric potential of a double-gated (DG) fully depleted (FD) junctionless (J-less) transistor by solving the two-dimensional Poisson's equation. On the basis of this two-dimensional electric potential model, subthreshold current and swing can be calculated. Threshold voltage roll-off can also be estimated with analytical forms derived using the above model. The calculated results of electric potential, subthreshold current and threshold voltage roll-off are all in good agreement with the results of technology computer aided design (TCAD) simulation. The model proposed in this paper may help in the development of a compact model for simulation program with integrated circuit emphasis (SPICE) simulation and in providing deeper insights into the characteristics of short-channel J-less transistors.