The archimedean family are the most popular parametric families of copulas. In the present paper, we propose a new generalization of Archimedean copulas with two dependence parameters. The model is based on the bivariate Gumbel-Barnett distribution. At first we introduced the generalized model that is defined by using the concave multiplicative generators in the style of FGM family (in details, see Doodman et al. (2021) †), which is named AFGM copula, then we introduced the new model. Some examples of the parametric subfamilies are provided which show that these families cover a wide range of dependencies rather than the corresponding Archimedean family. A real financial dataset study is used to illustrate the methodology and to compare the performance of this new generalized model with the corresponding AFGM copulas and Archimedean ones.

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