  Let $G$ be a simply connected solvable Lie group with a lattice $\Gamma$ and
$N$ the nilradical of $G$. For a complex valued representation $\rho: G\to
GL(V_{\rho})$ such that the restriction $\rho_{|_{N}}$ is unipotent, as an
advanced variation of cohomology computation of solvmanifolds by using Lie
algebra cohomology, we construct a explicit finite dimensional cochain complex
whose cohomology is isomorphic to the cohomology of $G/\Gamma$ with twisted by
$\rho$.
