Let $\Gamma$ be an Anosov subgroup of a connected semisimple real linear Lie group $G$. For a maximal horospherical subgroup $N$ of $G$, we show that the space of all non-trivial $NM$-invariant ergodic and $A$-quasi-invariant Radon measures on $\Gamma \backslash G$, up to proportionality, is homeomorphic to $\mathbb{R}^{\mathrm{rank} (G)-1}$, where $A$ is a maximal real split torus and $M$ is a maximal compact subgroup which normalizes $N$. \\ \\ This is joint work with Hee Oh.