For Neill mapping function,there are 26 mathematical operations for hydrostatic component and 11 operations for wet components need to be carried out in order to get the mapping function value. The Neill mapping function model for both hydrostatics and wet component are given in a form of continued fraction. In order to obtain fast results, the mapping function model need to be simplified. In this paper, the nonlinear curve fitting is used to simplify Neill Mapping Function model. Selection of model to be simplified is based on the model ability to reach mapping function value as low as 3 degree of elevation angle. To sum of error shows how close the simplified model result with the original model. The number of mathematical operation can be reduced after the process of simplification of the model. The percentage of reduction of operation for simplified model, especially for hydrostatic component is more than 80 percent. © 2016 Author(s).