One generalization of the Mellin integral transform in terms of pseudo-analysis is presented in the paper. Basic properties of this type of integral transform and one example are given. Both the g- Mellin convolution and the inverse g- Mellin transform are defined. The connections among the g- Mellin transform, the g- Mellin convolution and the inverse g- Mellin transform and the Mellin transform, as well as the connection between the Mellin convolution and the inverse Mellin transform are presented.