The possibility to explain the baryon asymmetry in the Universe through the leptogenesis mechanism in the context of Adjoint SU(5) is investigated. In this model the neutrino masses are generated through the Type I and Type III seesaw mechanisms, and the field responsible for the Type III seesaw, called rho_3, generates the B-L asymmetry needed to satisfy the observed value of the baryon asymmetry in the Universe. We find that the CP asymmetry originates only from the vertex correction, since the self-energy contribution is not present. When neutrino masses have a normal hierarchy, successful leptogenesis is possible for 10^{11} GeV < M_{\rho_3}^{NH} < 4 10^{14} GeV. When the neutrino hierarchy is inverted, the allowed mass range changes to 2 10^{11} GeV < M_{\rho_3}^{IH} < 5 10^{11} GeV. These constraints make possible to rule out a large part of the parameter space in the theory which was allowed by the unification of gauge interactions and the constraints coming from proton decay.