After a general consideration for the process of π+-photoproduction from proton, starting from the Mandelstam representation and using further the Cini-Fubini approximation, we derive the formulas for the isoscalar part of π-photoproduction amplitudes. According to new data on electromagnetic structure of nucleon, we choose the parameters of I=I=1 resonance of π-π interaction to be tr = 22, av= 1.52, bv= 1.60, and calculate (dσ)/(dΩ)(90°),(dσ‖)/(dσ⊥)(90°) and angular distributions at three energies. The results show that after introducing the π-π interaction the fit to the experiment is much improved over the results obtained by Chew et al. The coupling constant of γ+π→π + π is determined to be about ∧≈- 2.8 e, which is roughly consistent with the current results.