As a discussant of Arnold and Beaver (2002), Balakrishnan proposed a generalized skew-normal ($BSN$) distribution. This new model has been encountered in the literature for modeling various data sets. In this paper, we propose a new generalization of skew $t$-distribution of Azzalini and Capitanio (2003), denoted by $BST$, as a scale mixture of the $BSN$-distribution. This new model may be used for modeling data sets exhibiting a unimodal density function having some skewness as well as heavy tails with respect to the skew normal distribution. An explicit expression for the probability density function and a recurrence formula for the cumulative distribution function of the $BST$-distribution are derived. Some statistical characteristics of the proposed model including central moments, unimodality and stochastic orders are investigated. Two representation theorems for BST-distribution which may be used for generating copies from the new model are given. The problem of estimation of the unknown parameters on the basis of a random sample arising from $BST$-distribution are considered. For illustration proposes, a real data set on strength of glass fibres, due to Smith and Naylor (1987), is analyzed using the procedures obtained.

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