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The coupling of baryonic current to the derivative of the curvature scalar, <i>R</i>, inherent to gravitational baryogenesis (GBG), leads to a fourth-order differential equation of motion for <i>R</i> 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 the modification of gravity, introducing an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> term into the canonical action of GR. It is shown that this mechanism allows for the stabilization of GBG with bosonic and fermionic baryon currents. We establish the region of the model parameters leading to the stabilization of <i>R</i>. Still, the standard cosmology would be noticeably modified.