Let $X$ be a compact Kähler manifold, $x\in X$ be a base point and $\rho :{\pi }_1(X,x)\to G{L}_N\left(C\right)$ be the monodromy representation of a $𝒞$-VHS. Building on Goldman–Millson’s classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at $\rho$ and a variation of mixed Hodge structures whose monodromy is the universal deformation of $\rho$.