This paper presents a new multivariate elliptical distribution, namely the multivariate generalized Gamma times an Uniform (MGGU) distribution. Because it generalizes the multivariate generalized Gaussian distribution (MGGD), the MGGU distribution is able to fit a wider range of signals. For the bivariate case, we provide a closed-form of the Kullback-Leibler divergence (KLD). We propose the MG$\Gamma$U distribution for modeling chrominance wavelet coefficients and exercise it in a texture retrieval experiment. A comparative study between some multivariate models on the VisTex and Outex image database is conducted and reveals that the use of the MGGU distribution of chromiance wavelet coefficient allows an indexing gain compared to other classical approaches such as MGGD and Copula based model.