We search for electron anti-neutrinos ($overline{ u}_e$) from long and short-duration gamma-ray bursts~(GRBs) using data taken by the KamLAND detector from August 2002 to June 2013. No statistically significant excess over the background level is found. We place the tightest upper limits on $overline{ u}_e$ fluence from GRBs below 7 MeV and place first constraints on the relation between $overline{ u}_e$ luminosity and effective temperature.