Abstract: To characterize the anisotropic behavior of infinite-dimensional Banach space-valued functions, generalized Young functions on the product space of a Euclidean space and an infinite-dimensional Banach space are introduced, and their fundamental properties are investigated. Based on these generalized Young functions, a class of anisotropic Musielak-Orlicz spaces of Banach space-valued functions is constructed. The completeness of the resulting spaces is subsequently established. Furthermore, the corresponding dual spaces are characterized. These results enrich the theory of Banach space-valued Musielak-Orlicz spaces and provide a theoretical foundation for further studies of anisotropic function spaces.