We study whether the nonmonotonic behavior found in the differential cross section of the phi-meson
photoproduction off the proton near threshold can be described by a resonance. Namely, we add a resonance to a model consisting of Pomeron and (pi, eta) exchange by fiat and see if, with a suitable assignment of spin and
parity, mass and width, as well as the coupling constants, one would be able to obtain a good description
to all the data reported by the LEPS Collaboration in the low-energy region. The resonant contribution is
evaluated by using an effective Lagrangian approach. We find that, with the assumption of a resonance with spin 3/2
of both parities, LEPS data can indeed be well described. The ratio of the helicity amplitudes A _{1/2}/A_{3/2} calculated from the resulting coupling constants is quite similar to that of D13(2120) listed by PDG. We also perform a consistency check by applying our results to incoherent phi-meson photoproduction off the deuteron and found that without fitting to the data, we found a very good agreement. Moreover, we also present a prediction on the single and double polarization observables with the hope of resolving the
ambiguity on the parity of the resonance.