Based on the character in which both the intermediate and final states are intimately related with the vacuum properties of strong-interactions,we have discussed from an alternative point of view the processes of both the radiative production of glueball and the annihilation into electron-positron pair in J/ψ decays.Using the modified field theory model of pomeron in high-energy soft strong processes and the consequent hypothesis of the maximum non-perturbative strong interaction as well as the relevant changes of parameters of the model connecting with the large inner-structure difference between light and heavy constituent quarks,we proposed another mechanism for these two decay processes and calculated their partial width.The coupling constant between the glueballs and the non-perturbative gluons has been estimated.