A search for $K^-pp$ bound state (the lightest kaonic nucleus) has been performed using the $gamma d rightarrow K^+ pi^- rm{X}$ reaction at E$_gamma$=1.5-2.4 GeV at LEPS/SPring-8. The differential cross section of $K^+ pi^-$ photo-production off deuterium has been measured for the first time in this energy region, and a bump structure was searched for in the inclusive missing mass spectrum. A statistically significant bump structure was not observed in the region from 2.22 to 2.36 GeV/$c^2$, and the upper limits of the differential cross section for the $K^-pp$ bound state production were determined to be 0.1$-$0.7 $mu$ b (95$%$ confidence level) for a set of assumed binding energy and width values.
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