We take the X(1835) as a pseudoscalar baryonium state, and calculate the mass spectrum of the baryon-antibaryon bound states pp, ΣΣ, ΞΞ, and ΛΛ in the framework of the Bethe-Salpeter equation with a phenomenological potential. The numerical results indicate the pp, ΣΣ and ΞΞ bound states may exist, and the X(1835) can be tentatively identified as the pp bound state.