Effects of the (γ, 3π) vertex in the reaction γ+ p →p + 2π0 is studied. It is shown that the (γ, 3π)-part of the amplitude for this reaction is given by the “meson current part” of the amplitude for the single π0 production by a virtual photon, multiplied by a certain numerical factor including the effective coupling constant of the (γ, 3π) vertex. Thus referring to the theory of Fubini, Nambu and Wataghin for the single pion electroproduction, the (γ, 3π)-part of the double π0 photoproduction amplitude can be obtained almost exactly. It is also shown that, under appropriate experimental conditions, the major contribution to the reaction γ+ p →p + 2π0 comes from the absorption of the incident photons via the (γ, 3π) vertex, unless its effective coupling constant λ be much smaller than the value expected from the simple perturbation calculation. Thus, the experimental study of this reaction would possibly provide an alternative and rather unambiguous method for the determination of λ. An example for such a measurement is proposed, and the cross section under the proposed conditions is calculated.