In this paper, we introduce a new distribution as a scale mixture of the generalized half normal (GHN) distribution proposed by  and the generalized gamma (GG) distribution. Since the half-t (HT) distribution given in  is a special case of the new distribution, we call the new distribution as "generalized half-t (GHT)" distribution. We derive the probability density function (pdf) of the GHT distribution and study some of its properties. We give maximum likelihood (ML) estimators for its parameters based on the Expectation-Maximization (EM) algorithm. We provide a small simulation study to show the performances of the ML estimators for GHT distribution. Also, we give a real data example to illustrate the modeling performance of the proposed distribution over the GHN and HT distributions.