Wishart natural exponential families (NEFs) characterized by Letac (1989) are extended to the Riesz NEFs on symmetric matrices. These families are characterized by their variance functions defined in Hassairi and Lajmi (2001). This work uses a particular basis of these NEFs to describe the class of the generalized multivariate gamma distributions and then to study the statistical model obtained by the mixture of this distribution with the Riesz one on the space of symmetric matrices.