In this work, a compact model for MOSFET-like ballistic carbon nanotube field-effect transistors is presented. The model is based on calculating the charge and surface potential on the top of the barrier between source and drain using closed-form analytical formulae. The formula for the surface potential is obtained by merging two simplified expressions obtained in two extreme cases (very low and very high gate bias). Two fitting parameters are introduced whose values are extracted by best fitting model results with numerically-calculated ones. The model has a continuous derivative and thus is Spice-compatible. Accuracy of the model is compared to previous analytical model presented in the literature with numerical results taken as a reference. Proposed model proves to give less relative error over a wide range of gate bias, and for a drain bias up to 0.5 V. In addition, the model enables the calculation of quantum and gate capacitance analytically reproducing the negative capacitance behavior known in CNFETs.