  The coupling of baryonic current to the derivative of the curvature scalar,
$R$, inherent to gravitational baryogenesis (GBG), leads to a fourth order
differential equation of motion for $R$ instead of the algebraic one of General
Relativity (GR). The fourth-order differential equation is generically
unstable. We consider a possible mechanism of stabilization of GBG by
modification of gravity, introducing an $R^2$-term into the canonical action of
GR.
  It is shown that this mechanism allows for stabilization of GBG with bosonic
and fermionic baryon currents. We have established the region of the model
parameters leading to stabilization of $R$. Still, the standard cosmology would
be noticeably modified.
