A bathtub vortex is considered as one of significant phenomena which may cause gas entrainment (GE) in several industrial scenes, e.g. sodium-cooled fast reactors. In past studies, well-known Burgers vortex model is frequently used to simulate the bathtub vortex behavior. However, the Burgers model has a simple and unreal assumption that the axial velocity component is horizontally constant, while in real the bathtub vortex has the axial velocity distribution which shows large gradient in radial direction near the vortex center. In this study, a new theoretical vortex model with realistic axial velocity distribution is proposed. This model is derived from the axisymmetric Navier-Stokes equation as well as the Burgers model, but the axial velocity distribution in radial direction is considered. This function is defined to be zero at the vortex center and to approach asymptotically to zero at infinity. As the validation tests, the new model is applied to the evaluation of two simple vortex experiments and shows good agreements with the experimental data in terms of the free surface shape when the axial velocity distribution is modeled accurately. Therefore, it is confirmed that the accurate axial velocity modeling is crucially important to evaluate a bathtub vortex.