  The Chern-Simons-like gravitational action is evaluated explicitly in four
dimensional space-time by radiative corrections at one-loop level. The
calculation is performed in fermionic sector where the Dirac fermions interact
with the background gravitational field, including the parity-violating term
\bar\psi \bs\gamma_5\psi. The investigation takes into account the weak field
approximation and dimensional regularization scheme.
