  The gravitational baryogenesis plays an important role in the study of the
baryon asymmetry. However, the original mechanism of gravitational baryogenesis
in the radiation dominated era leads to the asymmetry factor $\eta$ is equal to
zero, which indicates this mechanism may not generate a sufficient baryon
asymmetry for the standard cosmological model. In this manuscript, we
investigate the gravitational baryogenesis for the generation of baryon
asymmetry in the early Universe by using an new higher-order generalized
uncertainty principle (GUP). It is demonstrated that the entropy and Friedman
equation of the Universe deviate from the original cases due to the effect of
the higher-order GUP. Those modifications break the thermal equilibrium of the
Universe and in turn produces a non-zero asymmetry factor $\eta $. In
particular, our results satisfy all three Sakharov conditions, which indicates
that the scheme of explaining baryon asymmetry in the framework of higher-order
GUP is feasible. In addition, confronting our theoretical results with the
observational results, we constraint the GUP parameter $\beta_0$, whose bound
between $8.4 \times {10^{10}} \sim 1.1 \times {10^{13}}$.
