  Scalar-tensor $f(R)$ theory of gravity is considered in the framework of a
simple inhomogeneous space-time model. In this we use the reconstruction
technique to look for possible evolving wormhole solutions within viable $f(R)$
gravity formalism. These $f(R)$ models are then constrained so that they are
consistent with existing experimental data. Energy conditions related to the
matter threading the wormhole are analysed graphically and are in general found
to obey the null energy conditions (NEC) in regions around the throat, while in
the limit $f(R)=R,$ NEC can be violated at large in regions around the throat.
