An analytical model is developed for the carrier density in MOSFET-like carbon nanotube field-effect transistors in terms of surface potential. This model is based on approximating the density of states with delta function in addition to a constant value. The model has a continuous derivative and contains two fitting parameters, which are determined by best fitting with numerical results. The fitting parameters are found to depend on the subband minima and this dependence is modeled by simple quadrature formula. The model is compared to two previous analytical models with numerical results are taken as a reference and found to have less relative error. In addition, the drain current is extracted using the proposed model at various bias values. The results for current are verified by comparison with self-consistent numerical results of FETToy simulator available on the NanoHub.