We study the decay process of J/psi e(+)e(-)phi where the relatively clean electromagnetic (EM) transitions appear at leading order at tree level while the hadronic contributions only emerge via hadronic loop transitions. We include the low-lying scalar f(0) (980) and pseudoscalar eta/eta' as the dominant contributions in the evaluation of the hadronic loop contributions. It is found that the hadronic effects are negligible compared with the EM contributions. The decay width of J/psi e(+)e(-)phi is determined to be about 2.12 x 10(-6) keV if there is no other leading mechanism contributing. This result will be tested by the BESIII experiment with a large J/psi data sample.