The mechanism of gravitational baryogenesis, based on the CP T -violating gravitational interaction between the derivative of the Ricci scalar curvature and the baryon-number current, is investigated in the context of the Gauss-Bonnet braneworld cosmology. We study the constraints on the fundamental five-dimensional gravity scale, the effective scale of B-violation and the decoupling temperature, for the above mechanism to generate an acceptable baryon asymmetry during the radiation-dominated era. The scenario of gravitational leptogenesis, where the lepton-number violating interactions are associated with the neutrino mass seesaw operator, is also considered.