  In this paper, we consider an obstruction-theoretical construction of
characteristic classes of fiber bundles by simplicial method. We can get a
certain obstruction class for a deformation of $C_\infty$-algebra models of
fibers and a characteristic map from the exterior algebra of a vector space of
derivations. Applying this construction for a surface bundle, we obtain the
Euler class of a sphere bundle and the Morita-Miller-Mumford classes of a
bundle with positive genus fiber.
