Silicon nanowire FET (SiNWFET) with dynamic polarity control has been experimentally demonstrated and has shown large potential in circuit applications. To fully explore its circuit-level opportunities, a physics-based compact model of the polarity-controllable SiNWFET is required. Therefore, in this paper, we extend the solution for conventional SiNWFETs to polarity-controllable SiNWFETs. By solving the current continuity equation, the potential distribution and drain current is obtained. The model shows good aoreement with TCAD simulation. It can be used as the core to develop the complete compact model for polarity-controllable SiNWFETs.