In the framework of the constituent quark model, the possible S-wave heavy dibaryon states with the c flavor are investigated. The factors which are responsible for the binding behavior of the dibaryon system are analyzed. It is shown that both the symmetry character of the system and the energy of interactions between interacting quarks are important for the binding behavior of the two-baryon system with the heavy flavor. As a result, seven possible candidates of heavy dibaryons with c flavor are predicted.