In this paper an analytic model for Ge/Si core/shell nanowire MOSFETs (NWFETs) is developed. First, the electrostatic potential and charge model are derived out from classical device physics. Then the drift-diffusion drain current model is obtained and verified by comparisons with the numerical simulation. The ballistic current model is obtained with the approximately described quantum-mechanical effect through modifying the intrinsic carrier concentration under 2-dimensional confinement. With the proposed model, the performances of Ge/Si core/shell NWFETs are analyzed and significant characteristics are demonstrated in details. The analytic model in this paper provides a framework for further developing compact models of the NWFETs with Ge/Si core/shell heterostructure for circuit design and simulation.