In the framework of the heavy baryon perturbation theory, in which the two-pion exchange is considered, the physical properties of heavy baryon and anti-heavy baryon systems are revisited. The potentials between heavy baryon and anti-heavy baryon are extracted in a holonomic form. Based on the extracted potentials, the S-wave scattering phase shifts and scattering lengths of Lambda(c)-(Lambda(c)) over bar and Sigma(c)-(Sigma(c)) over bar are calculated. From these scattering features, it is found that the Lambda(c)-(Lambda(c)) over bar system can be bound only when the value of the coupling constant at the baryon-Goldstone-boson vertex is larger than that calculated from the decay data of the Sigma(c)(Sigma c*) -> Lambda(c)pi process. The binding condition for the Sigma(c)-(Sigma(c)) over bar system is also examined. The binding possibilities of these systems deduced from the scattering calculations are also checked by the bound state calculation and the binding energies are obtained if the system can be really bound. The binding possibility of the Lambda(b)-(Lambda) over barb system is investigated as well.