In this paper an analytic channel potential-based model is proposed to predict the dynamic depletion behavior of surrounding-gate (SRG) MOSFETs with arbitrary doping level. The key input voltage equation is derived out by solving Poisson's equation approximately with arbitrary doping in the cylindrical coordinate. Combined with the surface-centric potential relationship, the electrostatic potential solution along the radius of both intrinsic and heavily doped SRG is obtained. With the potential solutions at the source and drain sides of the channel, the analytic drain current model is provided to calculate the current characteristics of the SRG MOSFET. The presented model can realize transition from partial depletion to full depletion of SRG MOSFET, which is validated by numerical simulation.