  Using the general method presented by Mohammedi \cite{NM} for the
integrability of a sigma model on a manifold, we investigate the conditions for
having an integrable deformation of the general sigma model on a manifold with
a complex structure. On a Lie group, these conditions are satisfied by using
the zeros of the Nijenhuis tensor. We then extend this formalism to a manifold,
especially a Lie group, with a generalized complex structure. We demonstrate
that, for the examples of integrable sigma models with generalized complex
structures on the Lie groups $\mathbf{A_{4,8}}$ and $\mathbf{A_{4,10}}$, under
special conditions, the perturbed terms of the actions are identical to the WZ
terms.
