We investigate a parametric calibration problem of the European call option prices using the exponential CGMY model. Option prices created using the CGMY model is calculated by the Fast Fourier Transform (FFT) proposed by P. Carr and D.B. Madan. In generally, the calibration process in the option pricing model is very hard because the objective function have the numerous local minimums across a broad parameter range. In this paper, we use the regularization method based on the four moments (the mean, variance, skewness, and kurtosis) for the CGMY model to conquer the ill-posed inverse problem. We shows the numerical implementation for the exponential CGMY model using the nonlinear optimization algorithm and shown that it is very useful method to resolve the instability of the calibration problem. In particular, we apply our approach to the KOSPI200 index options and show that our results significantly outperform than those for Black-Scholes option pricing model.