In this paper, we are dedicated to exemplifying a two parameter curve fitting method and developing a Matlab-based simulation program to extract the nonlinear refractive index and nonlinear absorption coefficient from closed-aperture Z-scan or R(z) data without the need for performing open-aperture Z-scan measurement. It should be noted, however, that both approaches can only be applicable to a case for which the on-axis phase shift at the focus is small. In this way, we not only determine the nonlinear parameters quickly with reasonable accuracy, as well as save time, efforts and equipment in the process of Z-scan implementation, but also obtain an initial estimate in order to compare with the results of the open-aperture Z-scan measurement when needed.