In this paper, we introduce the concepts of multi-generalized 2-normed space and dual multi-generalized 2-normed space and we then investigate some results related to them. We also prove that, if $(E,\|.,.\|)$ is a generalized 2-normed space, $\{\|.,.\|\}_{k\in\mathbb N}$ is a sequence of generalized 2-norms on $E^k$ $(k\in'\mathbb N)$ such that for each $x,y\in E$, $\|x,y\|_1=\|x,y\|$ and for each $k\in\mathbb N$ axioms $(MG1),(MG2)$ and $(MG4)(\ (DG4))$ of (dual) multi-generalized 2-normed space are true, then $\{(E^k,\|.,.\|_k),k\in\mathbb N\}$ is a (dual) multi-generalized 2-normed space. Finally we deal with an application of a dual multi-generalized 2-normed space defined on a proper commutative $H^*$-algebra.