Photoproduction of the neutral kaon on the deuteron has been investigated at the Research Center for Electron Photon Science, Tohoku University. We constructed the Neutral Kaon Spectrometer-2 for the detection of charged particles from the decay of the neutral kaon and the hyperon. We obtained a momentum distribution of K (0) with the inclusive measurement. It was consistent with the previous measurement. The total cross section of gamma + d -> K (0) + I > + p was estimated from the measured integral cross section of gamma + d -> I > + X. The total cross section with respect to the photon energy was compared with the theoretical calculations. It favored the Saclay-Lyon A model calculation with the ratio of the neutral to charged coupling constants of the axial-vector meson, K (1), as similar to -1.5. The energy dependence and the magnitude of the total cross section were similar to the total cross section of gamma + p -> K (+) Lambda.