  We describe the generalized Kuranishi spaces of solvmanifolds with
left-invariant complex structures. By using such description, we study the
stability of left-invariantness of deformed generalized complex structures and
smoothness of generalized Kuranishi spaces on certain classes of solvmanifolds.
We also give explicit finite dimensional cohcain complexes which computes the
holomorphic Poisson cohomology of nilmanifolds and solvmanifolds.
