Abstarct: In this thesis, we have studied a new generalization of Alpha-Skew Normal distribution, which is denoted by GASN (α , λ). in the chapter one, we have introduced the conceptes required in this thesis and then we illustrated normal and skew normal distributions. In the chapter two, we have introuced Alpha-Skew Normal distribution and som theorem about it. In the chapter tree, GASN (α , λ) distribution have been introduced and we have studied its properties, moments and maximun likelihood estimation of parameters. finally in chapter four by using R statistical software some features of previous theoretical problems will be explored. we show that our new distribution is the best fitted distribution for the used data among Normal, Skew Normal, Alpha -Skew Normal and Skew Bimodal Normal distributions.