A carrier-based analytic drain current model including the velocity saturation effect for the undoped surrounding-gate (SRG) MOSFETs is developed in this paper. Based on the previously ideal carrier-based drain current model, the Caughey-Thomas mobility model with an exponent factor n = 2 is applied and integrated into the analytic drain current model development. The validity of the presented model is confirmed by comparisons with three-dimensional (3D) TCAD device simulations for good agreements between the model prediction and numerical simulation on transfer/output characteristics and trans/output-conductance of the SRG MOSFETs are obtained in the whole operation regions from subthreshold to strong inversion and from linear to saturation regions. The symmetry property of the developed drain current model is guaranteed by the exponent factor n = 2 in the Caughey-Thomas model and also further tested, promoting the analog circuit design function of the proposed model.