Exclusive cross sections for double-pion photoproductions on proton and deuteron were measured in an energy range from 0.8 to 1.1GeV using tagged photons at Laboratory of Nuclear Science, Tohoku University. We employed the Neutral Kaon Spectrometer (NKS) to detect two pions in the final state, and deduced the cross section for the π^+π^- photoproduction on the "free" and "bound" proton. We have discriminated between the quasi-free and non-quasi-free process applying the kinematical cut on the missing momentum. We found that the total cross section for the γ"p"→pπ^+π^- reaction was about 60% of that for the "free" proton, and this is consistent with the previously obtained data. The one of the dominant part of the non-quasi-free process was found to be the double Δ production. Its cross section is smaller than the previous investigations.