In this paper a new approach for performing Independent Component Analysis (ICA) is introduced. The Extended Generalized Lambda Distribution (EGLD) is employed for modeling source distributions. The major benefit of the EGLD is that it also takes into account the skewness of the distributions. We briefly review maximum likelihood approach in ICA and study how the parameters of EGLD may be estimated. The score function of EGLD based ICA is presented and algorithms for its maximization are proposed. The simulation examples illustrate that the proposed method reliably separates the sources in situations where some widely used contrast functions may perform poorly.